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Journal articles on the topic 'Fixed points of morphisms'

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Published: 10 December 2022
Last updated: 28 January 2023

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1

Ślosarski, Mirosław. "The Fixed Points of Abstract Morphisms." British Journal of Mathematics & Computer Science 4, no. 21 (January 10, 2014): 3077–89. http://dx.doi.org/10.9734/bjmcs/2014/12891.

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2

Shallit, Jeffrey, and Ming-wei Wang. "On two-sided infinite fixed points of morphisms." Theoretical Computer Science 270, no. 1-2 (January 2002): 659–75. http://dx.doi.org/10.1016/s0304-3975(01)00092-5.

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3

Constantinescu, Sorin, and Lucian Ilie. "The Lempel–Ziv Complexity of Fixed Points of Morphisms." SIAM Journal on Discrete Mathematics 21, no. 2 (January 2007): 466–81. http://dx.doi.org/10.1137/050646846.

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4

Levé, F., and G. Richomme. "On a conjecture about finite fixed points of morphisms." Theoretical Computer Science 339, no. 1 (June 2005): 103–28. http://dx.doi.org/10.1016/j.tcs.2005.01.011.

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5

Klouda, Karel, Kateřina Medková, Edita Pelantová, and Štěpán Starosta. "Fixed points of Sturmian morphisms and their derivated words." Theoretical Computer Science 743 (September 2018): 23–37. http://dx.doi.org/10.1016/j.tcs.2018.06.037.

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6

Holub, Štěpán. "Polynomial-time algorithm for fixed points of nontrivial morphisms." Discrete Mathematics 309, no. 16 (August 2009): 5069–76. http://dx.doi.org/10.1016/j.disc.2009.03.019.

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7

FREYDENBERGER, DOMINIK D., DANIEL REIDENBACH, and JOHANNES C. SCHNEIDER. "UNAMBIGUOUS MORPHIC IMAGES OF STRINGS." International Journal of Foundations of Computer Science 17, no. 03 (June 2006): 601–28. http://dx.doi.org/10.1142/s0129054106004017.

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We study a fundamental combinatorial problem on morphisms in free semigroups: With regard to any string α over some alphabet we ask for the existence of a morphism σ such that σ(α) is unambiguous, i.e. there is no morphism τ with τ(i) ≠ σ(i) for some symbol i in α and, nevertheless, τ(α) = σ(α). As a consequence of its elementary nature, this question shows a variety of connections to those topics in discrete mathematics which are based on finite strings and morphisms such as pattern languages, equality sets and, thus, the Post Correspondence Problem. Our studies demonstrate that the existence of unambiguous morphic images essentially depends on the structure of α: We introduce a partition of the set of all finite strings into those that are decomposable (referred to as prolix) in a particular manner and those that are indecomposable (called succinct). This partition, that is also known to be of major importance for the research on pattern languages and on finite fixed points of morphisms, allows to formulate our main result according to which a string α can be mapped by an injective morphism onto an unambiguous image if and only if α is succinct.
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8

Krieger, Dalia. "On Critical exponents in fixed points ofk-uniform binary morphisms." RAIRO - Theoretical Informatics and Applications 43, no. 1 (December 20, 2007): 41–68. http://dx.doi.org/10.1051/ita:2007042.

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9

Krieger, Dalia. "On critical exponents in fixed points of non-erasing morphisms." Theoretical Computer Science 376, no. 1-2 (May 2007): 70–88. http://dx.doi.org/10.1016/j.tcs.2007.01.020.

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10

Valyuzhenich, Alexander. "Permutation complexity of the fixed points of some uniform binary morphisms." Electronic Proceedings in Theoretical Computer Science 63 (August 17, 2011): 257–64. http://dx.doi.org/10.4204/eptcs.63.32.

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11

BERTHÉ, VALÉRIE, WOLFGANG STEINER, JÖRG M. THUSWALDNER, and REEM YASSAWI. "Recognizability for sequences of morphisms." Ergodic Theory and Dynamical Systems 39, no. 11 (January 24, 2018): 2896–931. http://dx.doi.org/10.1017/etds.2017.144.

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We investigate different notions of recognizability for a free monoid morphism $\unicode[STIX]{x1D70E}:{\mathcal{A}}^{\ast }\rightarrow {\mathcal{B}}^{\ast }$ . Full recognizability occurs when each (aperiodic) point in ${\mathcal{B}}^{\mathbb{Z}}$ admits at most one tiling with words $\unicode[STIX]{x1D70E}(a)$ , $a\in {\mathcal{A}}$ . This is stronger than the classical notion of recognizability of a substitution $\unicode[STIX]{x1D70E}:{\mathcal{A}}^{\ast }\rightarrow {\mathcal{A}}^{\ast }$ , where the tiling must be compatible with the language of the substitution. We show that if $|{\mathcal{A}}|=2$ , or if $\unicode[STIX]{x1D70E}$ ’s incidence matrix has rank $|{\mathcal{A}}|$ , or if $\unicode[STIX]{x1D70E}$ is permutative, then $\unicode[STIX]{x1D70E}$ is fully recognizable. Next we investigate the classical notion of recognizability and improve earlier results of Mossé [Puissances de mots et reconnaissabilité des points fixes d’une substitution. Theoret. Comput. Sci. 99(2) (1992), 327–334] and Bezuglyi et al [Aperiodic substitution systems and their Bratteli diagrams. Ergod. Th. & Dynam. Sys. 29(1) (2009), 37–72], by showing that any substitution is recognizable for aperiodic points in its substitutive shift. Finally we define recognizability and also eventual recognizability for sequences of morphisms which define an $S$ -adic shift. We prove that a sequence of morphisms on alphabets of bounded size, such that compositions of consecutive morphisms are growing on all letters, is eventually recognizable for aperiodic points. We provide examples of eventually recognizable, but not recognizable, sequences of morphisms, and sequences of morphisms which are not eventually recognizable. As an application, for a recognizable sequence of morphisms, we obtain an almost everywhere bijective correspondence between the $S$ -adic shift it generates, and the measurable Bratteli–Vershik dynamical system that it defines.
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12

RAMPERSAD, NARAD. "WORDS AVOIDING $\frac{7}{3}$-POWERS AND THE THUE–MORSE MORPHISM." International Journal of Foundations of Computer Science 16, no. 04 (August 2005): 755–66. http://dx.doi.org/10.1142/s0129054105003273.

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In 1982, Séébold showed that the only overlap-free binary words that are the fixed points of non-identity morphisms are the Thue–Morse word and its complement. We strengthen Séébold's result by showing that the same result holds if the term 'overlap-free' is replaced with '[Formula: see text]-power-free'. Furthermore, the number [Formula: see text] is best possible.
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13

Allouche, Jean-Paul, and Luca Q. Zamboni. "Algebraic Irrational Binary Numbers Cannot Be Fixed Points of Non-trivial Constant Length or Primitive Morphisms." Journal of Number Theory 69, no. 1 (March 1998): 119–24. http://dx.doi.org/10.1006/jnth.1997.2207.

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14

ZANTEMA, HANS. "TURTLE GRAPHICS OF MORPHIC SEQUENCES." Fractals 24, no. 01 (March 2016): 1650009. http://dx.doi.org/10.1142/s0218348x16500092.

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The simplest infinite sequences that are not ultimately periodic are pure morphic sequences: fixed points of particular morphisms mapping single symbols to strings of symbols. A basic way to visualize a sequence is by a turtle curve: for every alphabet symbol fix an angle, and then consecutively for all sequence elements draw a unit segment and turn the drawing direction by the corresponding angle. This paper investigates turtle curves of pure morphic sequences. In particular, criteria are given for turtle curves being finite (consisting of finitely many segments), and for being fractal or self-similar: it contains an up-scaled copy of itself. Also space-filling turtle curves are considered, and a turtle curve that is dense in the plane. As a particular result we give an exact relationship between the Koch curve and a turtle curve for the Thue–Morse sequence, where until now for such a result only approximations were known.
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15

Popov, Vladimir A. "Analytic Extension of Locally Given Riеmannian Manifold to Global Space." UNIVERSITY NEWS. NORTH-CAUCASIAN REGION. NATURAL SCIENCES SERIES, no. 2 (214) (June 30, 2022): 21–27. http://dx.doi.org/10.18522/1026-2237-2022-2-21-27.

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Let’s consider the Lie algebra 𝔤 of all Killing vector fields of a Riemannian analytic manifold, its stationary subalgebra 𝔥, the simply connected Lie group 𝐺 corresponding to the Lie algebra 𝔤 and the subgroup 𝐻 corresponding to the Lie subalgebra 𝔥. The set of left adjacent classes 𝐺𝐻⁄ forms a homogeneous manifold if and only If 𝐻 is closed in 𝐺. We study the properties of the Lie algebra 𝔤 and its subalgebra 𝔥 under which 𝐻 is closed in 𝐺. The following category of Riemannian analytic manifolds is also studied. The objects of this category are oriented Riemannian analytic manifolds having open subsets isometric to each other and, consequently, the same algebra 𝔤 of Killing vector fields. It is assumed that the algebra 𝔤 has no center. Morphisms of this category are locally isometric maps 𝑓:𝑀⟶𝑁 preserving orientation and Killing vector fields. Moreover, the maps 𝑓 are defined on the entire manifold 𝑀 with the exception of the set 𝑆 of codimension at least two, consisting of fixed points of orientation-preserving isometries between open subsets of the manifold 𝑀. This category has a univer-sally attractive object. This is a so-called quasi-complete manifold, which by definition is unextendable manifold that does not admit nontrivial orientation-preserving and vector Killing fields isometries between its open subsets. For an arbitrary Riemannian analytic metric, a pseudo-field Riemannian analytic manifold is defined. This is a simply connected manifold 𝑀 for which there is no locally isometric map 𝑓:𝑀⟶𝑁 define on the whole 𝑀 and preserving orientation and killing vector fields. Where 𝑁 is a simply connected Riemannian analytic manifold other than 𝑀.
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16

Bellamy, Gwyn, and Alastair Craw. "Birational geometry of symplectic quotient singularities." Inventiones mathematicae 222, no. 2 (April 30, 2020): 399–468. http://dx.doi.org/10.1007/s00222-020-00972-9.

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Abstract For a finite subgroup $$\Gamma \subset \mathrm {SL}(2,\mathbb {C})$$ Γ ⊂ SL ( 2 , C ) and for $$n\ge 1$$ n ≥ 1 , we use variation of GIT quotient for Nakajima quiver varieties to study the birational geometry of the Hilbert scheme of n points on the minimal resolution S of the Kleinian singularity $$\mathbb {C}^2/\Gamma $$ C 2 / Γ . It is well known that $$X:={{\,\mathrm{{\mathrm {Hilb}}}\,}}^{[n]}(S)$$ X : = Hilb [ n ] ( S ) is a projective, crepant resolution of the symplectic singularity $$\mathbb {C}^{2n}/\Gamma _n$$ C 2 n / Γ n , where $$\Gamma _n=\Gamma \wr \mathfrak {S}_n$$ Γ n = Γ ≀ S n is the wreath product. We prove that every projective, crepant resolution of $$\mathbb {C}^{2n}/\Gamma _n$$ C 2 n / Γ n can be realised as the fine moduli space of $$\theta $$ θ -stable $$\Pi $$ Π -modules for a fixed dimension vector, where $$\Pi $$ Π is the framed preprojective algebra of $$\Gamma $$ Γ and $$\theta $$ θ is a choice of generic stability condition. Our approach uses the linearisation map from GIT to relate wall crossing in the space of $$\theta $$ θ -stability conditions to birational transformations of X over $$\mathbb {C}^{2n}/\Gamma _n$$ C 2 n / Γ n . As a corollary, we describe completely the ample and movable cones of X over $$\mathbb {C}^{2n}/\Gamma _n$$ C 2 n / Γ n , and show that the Mori chamber decomposition of the movable cone is determined by an extended Catalan hyperplane arrangement of the ADE root system associated to $$\Gamma $$ Γ by the McKay correspondence. In the appendix, we show that morphisms of quiver varieties induced by variation of GIT quotient are semismall, generalising a result of Nakajima in the case where the quiver variety is smooth.
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17

Allouche, J. P., J. Betrema, and J. O. Shallit. "Sur des points fixes de morphismes d'un monoïde libre." RAIRO - Theoretical Informatics and Applications 23, no. 3 (1989): 235–49. http://dx.doi.org/10.1051/ita/1989230302351.

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18

Darmajid and Bernt Tore Jensen. "Varieties of complexes of fixed rank." Journal of Algebra and Its Applications 14, no. 05 (March 17, 2015): 1550077. http://dx.doi.org/10.1142/s0219498815500772.

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We study varieties of complexes of projective modules with fixed ranks, and relate these varieties to the varieties of their homologies. We show that for an algebra of global dimension at most two, these two varieties are related by a pair of morphisms which are smooth with irreducible fibers.
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19

Picavet, Gabriel. "Recent Progress on Submersions: A Survey and New Properties." Algebra 2013 (May 12, 2013): 1–14. http://dx.doi.org/10.1155/2013/128064.

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This paper is a survey about recent progress on submersive morphisms of schemes combined with new results that we prove. They concern the class of quasicompact universally subtrusive morphisms that we introduced about 30 years ago. They are revisited in a recent paper by Rydh, with substantial complements and key results. We use them to show Artin-Tate-like results about the 14th problem of Hilbert, for a base scheme either Noetherian or the spectrum of a valuation domain. We look at faithfully flat morphisms and get “almost” Artin-Tate-like results by considering the Goldman (finite type) points of a scheme. Bjorn Poonen recently proved that universally closed morphisms are quasicompact. By introducing incomparable morphisms of schemes, we are able to characterize universally closed surjective morphisms that are either integral or finite. Next we consider pure morphisms of schemes introduced by Mesablishvili. In the quasicompact case, they are universally schematically dominant morphisms. This leads us to a characterization of universally subtrusive morphisms by purity. Some results on the schematically dominant property are given. The paper ends with properties of monomorphisms and topological immersions, a dual notion of submersions.
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20

Farjoun, E. Dror, and A. Zabrodsky. "Fixed points and homotopy fixed points." Commentarii Mathematici Helvetici 63, no. 1 (December 1988): 286–95. http://dx.doi.org/10.1007/bf02566768.

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21

Fleischer, Lukas, and Manfred Kufleitner. "The complexity of weakly recognizing morphisms." RAIRO - Theoretical Informatics and Applications 53, no. 1-2 (November 15, 2018): 1–17. http://dx.doi.org/10.1051/ita/2018006.

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Weakly recognizing morphisms from free semigroups onto finite semigroups are a classical way for defining the class of ω-regular languages, i.e., a set of infinite words is weakly recognizable by such a morphism if and only if it is accepted by some Büchi automaton. We study the descriptional complexity of various constructions and the computational complexity of various decision problems for weakly recognizing morphisms. The constructions we consider are the conversion from and to Büchi automata, the conversion into strongly recognizing morphisms, as well as complementation. We also show that the fixed membership problem is NC1-complete, the general membership problem is in L and that the inclusion, equivalence and universality problems are NL-complete. The emptiness problem is shown to be NL-complete if the input is given as a non-surjective morphism.
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22

Fletcher, Alastair. "Fixed curves near fixed points." Illinois Journal of Mathematics 59, no. 1 (2015): 189–217. http://dx.doi.org/10.1215/ijm/1455203164.

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23

Boxer, Laurence, Ozgur Ege, Ismet Karaca, Jonathan Lopez, and Joel Louwsma. "Digital fixed points, approximate fixed points, and universal functions." Applied General Topology 17, no. 2 (October 3, 2016): 159. http://dx.doi.org/10.4995/agt.2016.4704.

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A. Rosenfeld [23] introduced the notion of a digitally continuous function between digital images, and showed that although digital images need not have fixed point properties analogous to those of the Euclidean spaces modeled by the images, there often are approximate fixed point properties of such images. In the current paper, we obtain additional results concerning fixed points and approximate fixed points of digitally continuous functions. Among these are several results concerning the relationship between universal functions and the approximate fixed point property (AFPP).
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24

Espínola, R., and W. A. Kirk. "FIXED POINTS AND APPROXIMATE FIXED POINTS IN PRODUCT SPACES." Taiwanese Journal of Mathematics 5, no. 2 (June 2001): 405–16. http://dx.doi.org/10.11650/twjm/1500407346.

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25

Hutz, Benjamin. "Determination of all rational preperiodic points for morphisms of PN." Mathematics of Computation 84, no. 291 (May 5, 2014): 289–308. http://dx.doi.org/10.1090/s0025-5718-2014-02850-0.

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26

Górniewicz, Lech, and Danuta Rozpłoch-Nowakowska. "The Lefschetz fixed point theory for morphisms in topological vector spaces." Topological Methods in Nonlinear Analysis 20, no. 2 (December 1, 2002): 315. http://dx.doi.org/10.12775/tmna.2002.039.

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27

Medková, Kateřina, Edita Pelantová, and Laurent Vuillon. "Derived sequences of complementary symmetric Rote sequences." RAIRO - Theoretical Informatics and Applications 53, no. 3-4 (July 2019): 125–51. http://dx.doi.org/10.1051/ita/2019004.

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Complementary symmetric Rote sequences are binary sequences which have factor complexity C(n) = 2n for all integers n ≥ 1 and whose languages are closed under the exchange of letters. These sequences are intimately linked to Sturmian sequences. Using this connection we investigate the return words and the derived sequences to the prefixes of any complementary symmetric Rote sequence v which is associated with a standard Sturmian sequence u. We show that any non-empty prefix of v has three return words. We prove that any derived sequence of v is coding of three interval exchange transformation and we determine the parameters of this transformation. We also prove that v is primitive substitutive if and only if u is primitive substitutive. Moreover, if the sequence u is a fixed point of a primitive morphism, then all derived sequences of v are also fixed by primitive morphisms. In that case we provide an algorithm for finding these fixing morphisms.
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28

Gathmann, Andreas, Michael Kerber, and Hannah Markwig. "Tropical fans and the moduli spaces of tropical curves." Compositio Mathematica 145, no. 1 (January 2009): 173–95. http://dx.doi.org/10.1112/s0010437x08003837.

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AbstractWe give a rigorous definition of tropical fans (the ‘local building blocks for tropical varieties’) and their morphisms. For a morphism of tropical fans of the same dimension we show that the number of inverse images (counted with suitable tropical multiplicities) of a point in the target does not depend on the chosen point; a statement that can be viewed as one of the important first steps of tropical intersection theory. As an application we consider the moduli spaces of rational tropical curves (both abstract and in some ℝr) together with the evaluation and forgetful morphisms. Using our results this gives new, easy and unified proofs of various tropical independence statements, e.g. of the fact that the numbers of rational tropical curves (in any ℝr) through given points are independent of the points.
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29

Antinucci, Andrea, Massimo Bianchi, Salvo Mancani, and Fabio Riccioni. "Suspended fixed points." Nuclear Physics B 976 (March 2022): 115695. http://dx.doi.org/10.1016/j.nuclphysb.2022.115695.

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30

Beklemishev, Lev D., Dick de Jongh, Franco Montagna, and Alessandra Carbone. "Provable Fixed Points." Journal of Symbolic Logic 58, no. 2 (June 1993): 715. http://dx.doi.org/10.2307/2275233.

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31

Zlobec, Sanjo. "Characterizing fixed points." Croatian Operational Research Review 8, no. 1 (April 15, 2017): 351–56. http://dx.doi.org/10.17535/crorr.2017.0022.

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32

Brown, Robert F., and Jack E. Girolo. "Isolating Fixed Points." American Mathematical Monthly 109, no. 7 (August 2002): 595. http://dx.doi.org/10.2307/3072425.

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33

Brown, Robert F., and Jack E. Girolo. "Isolating Fixed Points." American Mathematical Monthly 109, no. 7 (August 2002): 595–611. http://dx.doi.org/10.1080/00029890.2002.11919891.

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34

De Jongh, Dick, and Franco Montagna. "Provable Fixed Points." Zeitschrift für Mathematische Logik und Grundlagen der Mathematik 34, no. 3 (1988): 229–50. http://dx.doi.org/10.1002/malq.19880340307.

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35

PIAO, Yongjie. "Almost Fixed Points and Fixed Points on Locally FC-Spaces." Acta Analysis Functionalis Applicata 12, no. 1 (May 24, 2010): 27–32. http://dx.doi.org/10.3724/sp.j.1160.2010.00027.

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36

O'Regan, Donal. "Fixed points and random fixed points for α-Lipschitzian maps." Nonlinear Analysis: Theory, Methods & Applications 37, no. 4 (August 1999): 537–44. http://dx.doi.org/10.1016/s0362-546x(98)00071-6.

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37

Hutz, Benjamin. "Rational periodic points for degree two polynomial morphisms on projective space." Acta Arithmetica 141, no. 3 (2010): 275–88. http://dx.doi.org/10.4064/aa141-3-3.

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38

Girard, Martine, and Leopoldo Kulesz. "Computation of Sets of Rational Points of Genus-3 Curves via the Dem'Janenko–Manin Method." LMS Journal of Computation and Mathematics 8 (2005): 267–300. http://dx.doi.org/10.1112/s1461157000000991.

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AbstractThe authors construct two families of genus-3 curves defined over Q(t) with three independent morphisms to an elliptic curve of rank at most two. They give explicit examples of an application of the Dem'janenko-Manin method that completely determines both the set of the Q(t)-rational points of the curves under consideration, and the set of Q-rational points of some specialisations.
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39

MEAGHER, STEVE. "A SIMPLE PROOF OF CHEBOTAREV’S DENSITY THEOREM OVER FINITE FIELDS." Bulletin of the Australian Mathematical Society 98, no. 2 (July 12, 2018): 196–202. http://dx.doi.org/10.1017/s0004972718000448.

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We present a simple proof of the Chebotarev density theorem for finite morphisms of quasi-projective varieties over finite fields following an idea of Fried and Kosters for function fields. The key idea is to interpret the number of rational points with a given Frobenius conjugacy class as the number of rational points of a twisted variety, which is then bounded by the Lang–Weil estimates.
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40

Stouti, Abdelkader, and Abdelhakim Maaden. "Fixed points and common fixed points theorems in pseudo-ordered sets." Proyecciones (Antofagasta) 32, no. 4 (December 2013): 409–18. http://dx.doi.org/10.4067/s0716-09172013000400008.

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41

O’Regan, Donal. "Fixed points and random fixed points for weakly inward approximable maps." Proceedings of the American Mathematical Society 126, no. 10 (1998): 3045–53. http://dx.doi.org/10.1090/s0002-9939-98-04601-2.

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42

Espínola, Rafa, Pepa Lorenzo, and Adriana Nicolae. "Fixed points, selections and common fixed points for nonexpansive-type mappings." Journal of Mathematical Analysis and Applications 382, no. 2 (October 2011): 503–15. http://dx.doi.org/10.1016/j.jmaa.2010.06.039.

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43

Singh, S. L., and J. H. M. Whitfield. "Contractors and fixed points." Colloquium Mathematicum 55, no. 2 (1988): 219–28. http://dx.doi.org/10.4064/cm-55-2-219-228.

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44

Mathews, John, and Soo Tang Tan. "Some Interesting Fixed Points." Mathematics Magazine 63, no. 4 (October 1, 1990): 263. http://dx.doi.org/10.2307/2690951.

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45

Ingram, Stephen. "The Moral Fixed Points." Journal of Ethics and Social Philosophy 9, no. 1 (June 7, 2017): 1–6. http://dx.doi.org/10.26556/jesp.v9i1.167.

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46

Subathra, G., and G. Jayalalitha. "FIXED POINTS-JULIA SETS." Advances in Mathematics: Scientific Journal 9, no. 9 (August 25, 2020): 6759–63. http://dx.doi.org/10.37418/amsj.9.9.34.

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47

Liu, Zeqing, M. S. Khan, and H. K. Pathak. "On Common Fixed Points." gmj 9, no. 2 (June 2002): 325–30. http://dx.doi.org/10.1515/gmj.2002.325.

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48

Nalawade, Vidyadhar V., and Uttam P. Dolhare. "Some Fixed Points Theorems." International Journal of Engineering Research and Applications 07, no. 07 (July 2017): 51–56. http://dx.doi.org/10.9790/9622-0707045156.

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49

Gonçalves, Daciberg. "Fixed points ofS1-fibrations." Pacific Journal of Mathematics 129, no. 2 (October 1, 1987): 297–306. http://dx.doi.org/10.2140/pjm.1987.129.297.

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50

Buff, X. "Virtually repelling fixed points." Publicacions Matemàtiques 47 (January 1, 2003): 195–209. http://dx.doi.org/10.5565/publmat_47103_09.

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