Relevant bibliographies by topics / Square-tiled surfaces

Academic literature on the topic 'Square-tiled surfaces'

Author: Grafiati
Published: 25 May 2023
Last updated: 4 May 2024

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Journal articles on the topic "Square-tiled surfaces"

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Johnson, Charles C. "Cutting sequences on square-tiled surfaces." Geometriae Dedicata 190, no. 1 (February 9, 2017): 53–80. http://dx.doi.org/10.1007/s10711-017-0227-z.

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Hillairet, Luc. "Spectral decomposition of square-tiled surfaces." Mathematische Zeitschrift 260, no. 2 (November 22, 2007): 393–408. http://dx.doi.org/10.1007/s00209-007-0280-7.

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Hubert, Pascal, Samuel Lelièvre, Luca Marchese, and Corinna Ulcigrai. "The Lagrange spectrum of some square-tiled surfaces." Israel Journal of Mathematics 225, no. 2 (April 2018): 553–607. http://dx.doi.org/10.1007/s11856-018-1667-3.

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Chen, Dawei. "Square-tiled surfaces and rigid curves on moduli spaces." Advances in Mathematics 228, no. 2 (October 2011): 1135–62. http://dx.doi.org/10.1016/j.aim.2011.06.002.

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Shrestha, Sunrose T. "Counting Formulae for Square-tiled Surfaces in Genus Two." Annales Mathématiques Blaise Pascal 27, no. 1 (August 26, 2020): 83–123. http://dx.doi.org/10.5802/ambp.392.

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Colognese, Paul, and Mark Pollicott. "Minimizing entropy for translation surfaces." Conformal Geometry and Dynamics of the American Mathematical Society 26, no. 6 (August 17, 2022): 97–110. http://dx.doi.org/10.1090/ecgd/374.

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In this note we consider the entropy by Dankwart [On the large-scale geometry of flat surfaces, 2014, PhD thesis. https://bib.math.uni-bonn.de/downloads/bms/BMS-401.pdf] of unit area translation surfaces in the S L ( 2 , R ) SL(2, \mathbb R) orbits of square tiled surfaces that are the union of squares, where the singularities occur at the vertices and the singularities have a common cone angle. We show that the entropy over such orbits is minimized at those surfaces tiled by equilateral triangles where the singularities occur precisely at the vertices. We also provide a method for approximating the entropy of surfaces in the orbits.
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Wright, Alex. "Schwarz triangle mappings and Teichmüller curves: Abelian square-tiled surfaces." Journal of Modern Dynamics 6, no. 3 (2012): 405–26. http://dx.doi.org/10.3934/jmd.2012.6.405.

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Lidjan, Edin, and Ðordje Baralic. "Homology of polyomino tilings on flat surfaces." Applicable Analysis and Discrete Mathematics, no. 00 (2021): 31. http://dx.doi.org/10.2298/aadm210307031l.

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The homology group of a tiling introduced by M. Reid is studied for certain topological tilings. As in the planar case, for finite square grids on topological surfaces, the method of homology groups, namely the non-triviality of some specific element in the group allows a ?coloring proof? of impossibility of a tiling. Several results about the non-existence of polyomino tilings on certain square-tiled surfaces are proved in the paper.
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Vincent DELECROIX, Elise GOUJARD, Peter ZOGRAF, Anton ZORICH, and Philip ENGEL. "Contribution of one-cylinder square-tiled surfaces to Masur-Veech volumes." Astérisque 415 (2020): 223–74. http://dx.doi.org/10.24033/ast.1107.

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Vincent DELECROIX, Elise GOUJARD, Peter ZOGRAF, Anton ZORICH, and Philip ENGEL. "Contribution of one-cylinder square-tiled surfaces to Masur-Veech volumes." Astérisque 415 (2020): 223–74. http://dx.doi.org/10.24033/ast.11107.

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Dissertations / Theses on the topic "Square-tiled surfaces"

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Cheboui, Smail. "Intersection Algébrique sur les surfaces à petits carreaux." Electronic Thesis or Diss., Montpellier, 2021. http://www.theses.fr/2021MONTS006.

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ON étudie la quantité notée Kvol définie par KVol(X,g) = Vol(X,g)*sup_{alpha,beta} frac{Int(alpha,beta)}{l_g (alpha)l_g(beta)} où X est une surface compacte de genre s, Vol(X,g) est le volume (l'aire) de la surface par rapport à la métrique g et alpha, beta deux courbes simples fermées sur la surface X. Les résultats principaux de cette thèse se trouvent dans les chapitres 3 et 4. Dans le chapitre 3 intitulé "Algebraic intersection for translation surfaces in the stratum H(2)" on s'intéresse à la suite des kvol des surfaces L(n,n) et on montre que KVol(L(n,n)) tend vers 2 quand n tend vers l'infini.Dans le chapitre 4 intitulé "Algebraic intersection for translation surfaces in a family of Teichmüller disks" on s'intéresse au Kvol des surfaces appartenant à la strate H(2s-2) qui sont des revêtements ramifiés à n feuillets d'un tore plat. On s'intéresse aussi aux surfaces St(2s-1) et on montre que kvol(St(2s-1))=2s-1 où s est le genre de la surface St(2s-1). On s'intéresse aussi au minimum du Kvol sur le disque de Teichmüller de la surface St(2s-1) qui sera (2s-1)sqrt{frac{143}{144}} et il est atteint aux deux points (pm frac{9}{14}, frac{sqrt{143}}{14})
We study the quantity denoted Kvol defined by KVol(X,g) = Vol(X,g)*sup_{alpha,beta} frac{Int(alpha,beta)}{l_g (alpha)l_g(beta)} where X is a compact surface of genus s, Vol(X,g) is the volume (area) of the surface with respect to the metric g and alpha, beta two simple closed curves on the surface X.The main results of this thesis can be found in Chapters 3 and 4. In Chapter 3 titled "Algebraic intersection for translation surfaces in the stratum H(2)" we are interested in the sequence of kvol of surfaces L(n,n) and we provide that KVol(L(n,n)) goes to 2 when n goes to infinity. In Chapter 4 titled "Algebraic intersection for translation surfaces in a family of Teichmüller disks" we are interested in the Kvol for a surfaces belonging to the stratum H(2s-2) wich is an n-fold ramified cover of a flat torus. We are also interested in the surfaces St(2s-1) and we show that kvol(St(2s-1))=2s-1. We are also interested in the minimum of Kvol on the Teichmüller disk of the surface St(2s-1) which will be (2s-1)sqrt {frac {143}{ 144}} and it is achieved at the two points (pm frac{9}{14}, frac{sqrt{143}}{14})
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Gatse, Franchel. "Spectre ordonné et branches analytiques d'une surface qui dégénère sur un graphe." Electronic Thesis or Diss., Orléans, 2020. http://www.theses.fr/2020ORLE3205.

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Dans ce travail, nous donnons un cadre général de surfaces riemanniennes qui dégénèrent sur des graphes métriques que nous appelons surfaces décomposables en cylindres et en jonctions. Les surfaces décomposables en cylindres et en jonctions dépendent d’un paramètre t qui traduit le mécanisme d’écrasement sur le graphe. Quand le paramètre t tend vers 0, les circonférences des cylindres tendent vers 0 et leurs longueurs restent fixes. On obtient ainsi les arêtes du graphe limite. Les jonctions, elles, sont écrasées dans toutes les directions et donc dégénèrent sur les sommets du graphe limite. Nous étudions alors le comportement asymptotique du spectre de ces variétés lors de cette déformation. Nous adoptons les points de vue de la convergence des valeurs propres ordonnées et de celle des branches analytiques. Ces deux approches sont fondamentalement différentes. Le cas des valeurs propres ordonnées est assez classique et nous retrouvons la convergence vers le spectre du graphe limite. L’étude des branches analytiques est plus original. Nous montrons la convergence et donnons une caractérisation des limites possibles. Ces résultats s’appliquent dans le cas des surfaces de translations qui possèdent une direction complètement périodique
In this work, we give a general framework of Riemannian surfaces that can degenerate on metric graphs and that we call surfaces made from cylinders and connecting pieces. The latter depend on a parameter t that describes the degeneration. When t goes to 0, the waists of the cylinders go to 0 but their lengths stay fixed. We thus obtain the edges of the limiting graph. The connecting pieces are squeezed in all directions and degenerate on the vertices of the limiting graph. We then study the asymptotic behaviour of the spectrum of these surfaces when t varies from two different points of view, considering the spectrum either as a sequence of ordered eigenvalues or as a collection of analytic eigenbranches. In the case of ordered eigenvalues, we recover a rather classical statement, and prove that the spectrum converges to the spectrum of the limiting object. The study of the analytic eigenbranches is more original. We prove that any such eigenbranch converges and we give a characterisation of the possible limits. These results apply to translation surfaces on which there is a completely periodic direction
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Gutiérrez, Rodolfo. "Combinatorial theory of the Kontsevich–Zorich cocycle." Thesis, Sorbonne Paris Cité, 2019. https://theses.md.univ-paris-diderot.fr/GUTIERREZ_Rodolfo_2_complete_20190408.pdf.

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En ce travail, trois questions liées au cocycle de Kontsevich–Zorich dans l'espaces de modules des différentielles quadratiques sont étudies avec des techniques combinatoires.Les deux premières impliquent la structure des groupes de Rauzy–Veech des différentielles abéliennes et quadratiques, respectivement. Ces groupes encodent l'action homologique des orbites presque fermées du flot géodésique de Teichmüller dans une composante connexe donnée d'une strate via le cocycle de Kontsevich–Zorich. Pour le cas abélien, on classifie complètement ces groupes et on montre qu'ils sont des sous-groupes explicites des groupes symplectiques, et qu'ils sont commensurables avec des réseaux arithmétiques. Pour le cas quadratique, on montre qu'ils sont aussi commensurables avec des réseaux arithmétiques si certaines conditions sur les ordres des singularités sont satisfaites.La troisième question implique la réalisabilité de certain groupes algébriques comme adhérences de Zariski des groupes de monodromie des surfaces à petits carreaux. En fait, on montre que quelques groupes de la forme SO*(2d) sont réalisables comme telles adhérences
In this work, three questions related to the Kontsevich--Zorich cocycle in the moduli space of quadratic differentials are studied by using combinatorial techniques.The first two deal with the structure of the Rauzy--Veech groups of Abelian and quadratic differentials, respectively. These groups encode the homological action of almost-closed orbits of the Teichmüller geodesic flow in a given component of a stratum via the Kontsevich--Zorich cocycle. For Abelian differentials, we completely classify such groups, showing that they are explicit subgroups of symplectic groups that are commensurable to arithmetic lattices. For quadratic differentials, we show that they are also commensurable to arithmetic lattices of symplectic groups if certain conditions on the orders of the singularities are satisfied.The third question deals with the realisability of certain algebraic groups as Zariski-closures of monodromy groups of square-tiled surfaces. Indeed, we show that some groups of the form SO*(2d) are realisable as such Zariski-closures
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Cabrol, Jonathan. "Origamis infinis : groupe de veech et flot linéaire." Thesis, Aix-Marseille, 2012. http://www.theses.fr/2012AIXM4323/document.

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Un origami, ou encore une surface à petits carreaux, est l'exemple le plus simple d'une surface de translation. Il s'obtient en collant entre eux un nombre fini de carreaux identiques. Le point le plus intéressant est l'étude du flot linéaire sur un origami, qui est un système dynamique continu lié à la dynamique des billards ou encore celle des échanges d'intervalles. Nous pouvons aussi nous intéresser au stabilisateur de l'action naturelle du groupe spécial linéaire sur les origamis, que nous appelons groupe de Veech de l'origami. Le but de cette thèse est l'étude de ces deux notions sur des exemples d'origamis infinis, obtenus en collant une infinité dénombrable de carreaux entre eux. Ces exemples sont obtenus comme revêtement galoisiens d'origamis finis, avec comme groupe de Galois des groupes abéliens, nilpotents ou plus compliqués
An origami, or a square-tiled surface, is the simplest example of translation surface. An origami can be viewed as a finite collection of identical squares, glued together along their edges. We can study the linear flow on this origami, which is the geodesic flow for this kind of surfaces. This dynamical system is related to the dynamical system of billiard, or interval exchange transformations. We can also study the Veech group of an origami. The special linear group acts on the space of translation surface, and the Veech group of an origami is the stabilizer of this origami under this action. We know in particular that the Veech group is a fuchsian group. In this thesis, we work on some example of infinite origamis. These origamis are constructed as Galois covering of finite origamis. In these examples, the deck group will be an abelian group, a niltpotent group or something more difficult
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Book chapters on the topic "Square-tiled surfaces"

1

Erlandsson, Viveka, and Juan Souto. "Counting Square-Tiled Surfaces." In Progress in Mathematics, 159–67. Cham: Springer International Publishing, 2022. http://dx.doi.org/10.1007/978-3-031-08705-9_10.

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Zorich, Anton. "Square Tiled Surfaces and Teichmüller Volumes of the Moduli Spaces of Abelian Differentials." In Rigidity in Dynamics and Geometry, 459–71. Berlin, Heidelberg: Springer Berlin Heidelberg, 2002. http://dx.doi.org/10.1007/978-3-662-04743-9_25.

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