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Articoli di riviste sul tema "Ergodic theory"

Autore: Grafiati

Pubblicato: 4 giugno 2021

Ultima modifica: 29 luglio 2024

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1

Gray, R. M. "Ergodic theory". Proceedings of the IEEE 74, n. 2 (1986): 380. http://dx.doi.org/10.1109/proc.1986.13473.

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2

Kida, Yoshikata. "Ergodic group theory". Sugaku Expositions 35, n. 1 (7 aprile 2022): 103–26. http://dx.doi.org/10.1090/suga/470.

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3

Moore, Calvin C. "Ergodic theorem, ergodic theory, and statistical mechanics". Proceedings of the National Academy of Sciences 112, n. 7 (17 febbraio 2015): 1907–11. http://dx.doi.org/10.1073/pnas.1421798112.

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This perspective highlights the mean ergodic theorem established by John von Neumann and the pointwise ergodic theorem established by George Birkhoff, proofs of which were published nearly simultaneously in PNAS in 1931 and 1932. These theorems were of great significance both in mathematics and in statistical mechanics. In statistical mechanics they provided a key insight into a 60-y-old fundamental problem of the subject—namely, the rationale for the hypothesis that time averages can be set equal to phase averages. The evolution of this problem is traced from the origins of statistical mechanics and Boltzman's ergodic hypothesis to the Ehrenfests' quasi-ergodic hypothesis, and then to the ergodic theorems. We discuss communications between von Neumann and Birkhoff in the Fall of 1931 leading up to the publication of these papers and related issues of priority. These ergodic theorems initiated a new field of mathematical-research called ergodic theory that has thrived ever since, and we discuss some of recent developments in ergodic theory that are relevant for statistical mechanics.

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4

JONES, ROGER L., ROBERT KAUFMAN, JOSEPH M. ROSENBLATT e MÁTÉ WIERDL. "Oscillation in ergodic theory". Ergodic Theory and Dynamical Systems 18, n. 4 (agosto 1998): 889–935. http://dx.doi.org/10.1017/s0143385798108349.

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In this paper we establish a variety of square function inequalities and study other operators which measure the oscillation of a sequence of ergodic averages. These results imply the pointwise ergodic theorem and give additional information such as control of the number of upcrossings of the ergodic averages. Related results for differentiation and for the connection between differentiation operators and the dyadic martingale are also established.

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5

Boyd, David W., Karma Dajani e Cor Kraaikamp. "Ergodic Theory of Numbers". American Mathematical Monthly 111, n. 7 (agosto 2004): 633. http://dx.doi.org/10.2307/4145181.

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6

Walters, Peter. "TOPICS IN ERGODIC THEORY". Bulletin of the London Mathematical Society 28, n. 2 (marzo 1996): 221–23. http://dx.doi.org/10.1112/blms/28.2.221.

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7

Sinai, Ya G., e Barry Simon. "Topics in Ergodic Theory". Physics Today 47, n. 10 (ottobre 1994): 74–75. http://dx.doi.org/10.1063/1.2808677.

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8

Barnes, Julie, Lorelei Koss e Rachel Rossetti. "The Ergodic Theory Café". Math Horizons 26, n. 3 (28 dicembre 2018): 5–9. http://dx.doi.org/10.1080/10724117.2018.1518099.

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9

Kozlov, V. V. "Coarsening in ergodic theory". Russian Journal of Mathematical Physics 22, n. 2 (aprile 2015): 184–87. http://dx.doi.org/10.1134/s1061920815020053.

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10

Jones, Roger L., Joseph M. Rosenblatt e Máté Wierdl. "Counting in Ergodic Theory". Canadian Journal of Mathematics 51, n. 5 (1 ottobre 1999): 996–1019. http://dx.doi.org/10.4153/cjm-1999-044-2.

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AbstractMany aspects of the behavior of averages in ergodic theory are a matter of counting the number of times a particular event occurs. This theme is pursued in this article where we consider large deviations, square functions, jump inequalities and related topics.

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11

Barnes, Julia, e Lorelei Koss. "The Ergodic Theory Carnival". Mathematics Magazine 83, n. 3 (giugno 2010): 180–90. http://dx.doi.org/10.4169/002557010x494823.

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12

Qi, Weiwei, Zhongwei Shen, Shirou Wang e Yingfei Yi. "Towards mesoscopic ergodic theory". Science China Mathematics 63, n. 9 (6 agosto 2020): 1853–76. http://dx.doi.org/10.1007/s11425-019-1642-5.

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13

Fivaz, Roland. "Ergodic theory of communication". Systems Research 13, n. 2 (giugno 1996): 127–44. http://dx.doi.org/10.1002/(sici)1099-1735(199606)13:2<127::aid-sres67>3.0.co;2-q.

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14

Biswas, HR, e MS Islam. "Ergodic theory of one dimensional Map". Bangladesh Journal of Scientific and Industrial Research 47, n. 3 (21 dicembre 2012): 321–26. http://dx.doi.org/10.3329/bjsir.v47i3.13067.

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In this paper we study one dimensional linear and non-linear maps and its dynamical behavior. We study measure theoretical dynamical behavior of the maps. We study ergodic measure and Birkhoff ergodic theorem. Also, we study some problems using Birkhoff's ergodic theorem. DOI: http://dx.doi.org/10.3329/bjsir.v47i3.13067 Bangladesh J. Sci. Ind. Res. 47(3), 321-326 2012

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15

ROY, EMMANUEL. "Poisson suspensions and infinite ergodic theory". Ergodic Theory and Dynamical Systems 29, n. 2 (aprile 2009): 667–83. http://dx.doi.org/10.1017/s0143385708080279.

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AbstractWe investigate the ergodic theory of Poisson suspensions. In the process, we establish close connections between finite and infinite measure-preserving ergodic theory. Poisson suspensions thus provide a new approach to infinite-measure ergodic theory. Fields investigated here are mixing properties, spectral theory, joinings. We also compare Poisson suspensions to the apparently similar looking Gaussian dynamical systems.

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16

Ellis, Robert. "Topological dynamics and ergodic theory". Ergodic Theory and Dynamical Systems 7, n. 1 (marzo 1987): 25–47. http://dx.doi.org/10.1017/s0143385700003795.

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AbstractIt is shown that when viewed properly some concepts in topological dynamics and ergodic theory are not merely analogous but equivalent. Also the Mackey-Halmos-von Neumann theorem on ergodic processes with discrete spectrum is generalized and an account of the Mackey-Zimmer theory of minimal cocycles is given in a more general setting.

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17

Mitkowski, Paweł, e Wojciech Mitkowski. "Ergodic theory approach to chaos: Remarks and computational aspects". International Journal of Applied Mathematics and Computer Science 22, n. 2 (1 giugno 2012): 259–67. http://dx.doi.org/10.2478/v10006-012-0019-4.

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Ergodic theory approach to chaos: Remarks and computational aspectsWe discuss basic notions of the ergodic theory approach to chaos. Based on simple examples we show some characteristic features of ergodic and mixing behaviour. Then we investigate an infinite dimensional model (delay differential equation) of erythropoiesis (red blood cell production process) formulated by Lasota. We show its computational analysis on the previously presented theory and examples. Our calculations suggest that the infinite dimensional model considered possesses an attractor of a nonsimple structure, supporting an invariant mixing measure. This observation verifies Lasota's conjecture concerning nontrivial ergodic properties of the model.

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18

Yuzvinsky, Sergey. "Rokhlin's School in ergodic theory". Ergodic Theory and Dynamical Systems 9, n. 4 (dicembre 1989): 609–18. http://dx.doi.org/10.1017/s0143385700005241.

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Ergodic theory is one of several fields of mathematics where the name Vladimir Abramovich Rokhlin (spelled also ‘Rochlin’ and ‘Rohlin’) is well known to the specialists. That name is attached to some very often used theorems, but the goal of this paper is not just to remind the reader of these theorems. I put them in the context of the general development of ergodic theory during the thirty years 1940–70. Most of all, I want to emphasize that Rokhlin was not only a researcher producing powerful results but also a founder of schools at the two best Universities in the USSR. For at least 10 years (1958–68) these schools dominated ergodic theory. This paper is not biographical. Rokhlin's life certainly deserves a better biographer. However, I mention certain circumstances of a non-mathematical nature where it seems to be appropriate.

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19

Bergelson, Vitaly, Nikos Frantzikinakis, Terence Tao e Tamar Ziegler. "Arbeitsgemeinschaft: Ergodic Theory and Combinatorial Number Theory". Oberwolfach Reports 9, n. 4 (2012): 2985–3059. http://dx.doi.org/10.4171/owr/2012/50.

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20

Ammari, Habib, Liliana Borcea, Thorsten Hohage e Barbara Kaltenbacher. "Arbeitsgemeinschaft: Ergodic Theory and Combinatorial Number Theory". Oberwolfach Reports 9, n. 4 (2012): 3061–127. http://dx.doi.org/10.4171/owr/2012/51.

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21

Svitek, Miroslav. "Wave probabilistic functions, entanglement and quasi-non-ergodic models". ECTI Transactions on Electrical Engineering, Electronics, and Communications 7, n. 2 (26 dicembre 2008): 55–62. http://dx.doi.org/10.37936/ecti-eec.200972.171892.

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The paper presents the theory of wave probabilistic models together with their important features like inclusion-exclusion rule, product rule and entanglement. These features are athematically described and the illustrative example is shown to demonstrate the possible applications of the theory. The presented theory can be also applied for modeling of quasi-non-ergodic probabilistic systems. First of all we show the new methodology on binary non-ergodic time series. The theory is extended into M-dimensional non-ergodic n-valued systems with linear ergodicity evolution that are called quasi-on-ergodic probabilistic systems.

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22

Johansson, Anders, Anders Öberg e Mark Pollicott. "Ergodic theory of Kusuoka measures". Journal of Fractal Geometry 4, n. 2 (2017): 185–214. http://dx.doi.org/10.4171/jfg/49.

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23

O'Malley. "Ergodic Theory and First Returns". Real Analysis Exchange 17, n. 1 (1991): 63. http://dx.doi.org/10.2307/44152185.

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24

ORNSTEIN, D. S. "Ergodic Theory, Randomness, and "Chaos"". Science 243, n. 4888 (13 gennaio 1989): 182–87. http://dx.doi.org/10.1126/science.243.4888.182.

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25

Weiss, Benjamin. "ALGEBRAIC IDEAS IN ERGODIC THEORY". Bulletin of the London Mathematical Society 24, n. 5 (settembre 1992): 505. http://dx.doi.org/10.1112/blms/24.5.505.

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26

Kitchens, Bruce. "Book Review: Computational ergodic theory". Bulletin of the American Mathematical Society 44, n. 01 (2 ottobre 2006): 147–56. http://dx.doi.org/10.1090/s0273-0979-06-01120-7.

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27

Feldman, Jack. "Book Review: Basic ergodic theory". Bulletin of the American Mathematical Society 33, n. 03 (1 luglio 1996): 345–47. http://dx.doi.org/10.1090/s0273-0979-96-00659-3.

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28

Ruelle, D. "Ergodic Aspects of Turbulence Theory". Physica Scripta T9 (1 gennaio 1985): 147–50. http://dx.doi.org/10.1088/0031-8949/1985/t9/024.

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29

Runde, Volker, e Ami Viselter. "Ergodic theory for quantum semigroups". Journal of the London Mathematical Society 89, n. 3 (25 aprile 2014): 941–59. http://dx.doi.org/10.1112/jlms/jdu015.

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30

Anosov, D. V. "Spectral multiplicity in ergodic theory". Proceedings of the Steklov Institute of Mathematics 290, S1 (15 settembre 2015): 1–44. http://dx.doi.org/10.1134/s0081543815070019.

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31

Kilochytska, Т. V. "Evolution of the Ergodic Theory". Nauka ta naukoznavstvo 4 (2019): 102–15. http://dx.doi.org/10.15407/sofs2019.04.102.

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32

Woś, Janusz. "Approximate Convergence in Ergodic Theory". Proceedings of the London Mathematical Society s3-53, n. 1 (luglio 1986): 65–84. http://dx.doi.org/10.1112/plms/s3-53.1.65.

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33

BOYARSKY, ABRAHAM, e PAWEŁ GÓRA. "AN ERGODIC THEORY OF CONSCIOUSNESS". International Journal of Bifurcation and Chaos 19, n. 04 (aprile 2009): 1397–400. http://dx.doi.org/10.1142/s0218127409023731.

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Abstract (sommario):

It has been suggested that the properties of "integration" and "differentiation" are necessary for the emergence of consciousness. We present a dynamical system model that is based on these two conditions. The collection of neurons are partitioned into clusters on which we define a map that reflects the communication between clusters. Such a map displays the forward and backward circuitry between clusters in a probabilistic manner. The presence of "re-entry" guarantees that the map is sufficiently complex, that is, nonlinear and chaotic, to possess numerous invariant sets of clusters, which are referred to as agglomerations. We suggest that an agglomeration that is mixing characterizes a conscious state. The model establishes a theoretical framework that may structure and encourage experimental work.

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34

Sinai, Ya G. "Kolmogorov's Work on Ergodic Theory". Annals of Probability 17, n. 3 (luglio 1989): 833–39. http://dx.doi.org/10.1214/aop/1176991249.

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35

Jones, Roger L., Iosif V. Ostrovskii e Joseph M. Rosenblatt. "Square functions in ergodic theory". Ergodic Theory and Dynamical Systems 16, n. 2 (aprile 1996): 267–305. http://dx.doi.org/10.1017/s0143385700008816.

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AbstractGiven the usual averages in ergodic theory, let n1 ≤ n2 ≤ … and . There is a strong inequality ‖Sf‖2 ≤ 25‖f‖2 and there is a weak inequality m{Sf > λ} ≤ (7000/λ)‖f‖1. Related results and questions for other variants of this square function are also discussed.

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36

Rota, Gian-Carlo. "Classification problems in ergodic theory". Advances in Mathematics 56, n. 3 (giugno 1985): 319. http://dx.doi.org/10.1016/0001-8708(85)90038-6.

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37

Rota, Gian-Carlo. "Ergodic theory and dynamical systems". Advances in Mathematics 56, n. 3 (giugno 1985): 319. http://dx.doi.org/10.1016/0001-8708(85)90040-4.

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38

Rota, Gian-Carlo. "Ergodic theory and related topics". Advances in Mathematics 59, n. 1 (gennaio 1986): 95. http://dx.doi.org/10.1016/0001-8708(86)90042-3.

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39

Rota, Gian-Carlo. "An introduction to ergodic theory". Advances in Mathematics 59, n. 2 (febbraio 1986): 184. http://dx.doi.org/10.1016/0001-8708(86)90052-6.

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40

Rota, Gian-Carlo. "Ergodic theory and differentiable dynamics". Advances in Mathematics 80, n. 2 (aprile 1990): 270. http://dx.doi.org/10.1016/0001-8708(90)90033-j.

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41

Lin, Dongdai, Tao Shi e Zifeng Yang. "Ergodic theory over F2〚T〛". Finite Fields and Their Applications 18, n. 3 (maggio 2012): 473–91. http://dx.doi.org/10.1016/j.ffa.2011.11.001.

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42

Saitô, Nobuhiko. "New concepts in ergodic theory". Vistas in Astronomy 37 (gennaio 1993): 137–39. http://dx.doi.org/10.1016/0083-6656(93)90023-d.

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43

Urbański, Mariusz, e Christian Wolf. "Ergodic Theory of Parabolic Horseshoes". Communications in Mathematical Physics 281, n. 3 (15 maggio 2008): 711–51. http://dx.doi.org/10.1007/s00220-008-0498-1.

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44

Thomine, Damien. "Keplerian shear in ergodic theory". Annales Henri Lebesgue 3 (30 luglio 2020): 649–76. http://dx.doi.org/10.5802/ahl.42.

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45

Kieffer, John C., e Y. Kifer. "Ergodic Theory of Random Transformations." Journal of the American Statistical Association 83, n. 402 (giugno 1988): 563. http://dx.doi.org/10.2307/2288883.

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46

Demir, Sakin. "Logarithmic Summability in Ergodic Theory". Journal of Computer and Mathematical Sciences 9, n. 5 (5 giugno 2018): 330–33. http://dx.doi.org/10.29055/jcms/779.

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47

Goldman, William M. "Ergodic Theory on Moduli Spaces". Annals of Mathematics 146, n. 3 (novembre 1997): 475. http://dx.doi.org/10.2307/2952454.

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48

Parczyk, Krystyna. "Ergodic theory and differentiable dynamics". Reports on Mathematical Physics 28, n. 3 (dicembre 1989): 439–41. http://dx.doi.org/10.1016/0034-4877(89)90074-8.

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49

Avigad, Jeremy. "The metamathematics of ergodic theory". Annals of Pure and Applied Logic 157, n. 2-3 (febbraio 2009): 64–76. http://dx.doi.org/10.1016/j.apal.2008.09.001.

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50

Chen, Mufa. "Eigenvalues, inequalities and ergodic theory". Chinese Science Bulletin 45, n. 9 (maggio 2000): 769–74. http://dx.doi.org/10.1007/bf02887400.

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