Sinai, Ya. G. (ed.), Dynamical Systems. II. Ergodic Theory with Applications to Dynamical Systems and Statistical Mechanics. Berlin etc. Springer-Verlag 1989. IX, 281 pp., 25 figs., DM 128.–. ISBN 3-540-17001-4 (Encyclopaedia of Mathematical Sciences 2)

1992 ◽  
Vol 72 (1) ◽  
pp. 58-58
Author(s):  
P. Möbius
Keyword(s):  
Dynamical Systems ◽  
Statistical Mechanics ◽  
Ergodic Theory ◽  
Mathematical Sciences

Randall Dougherty and Alexander S. Kechris. The complexity of antidifferentiation. Advances in mathematics, vol. 88 (1991), pp. 145–169. - Ferenc Beleznay and Matthew Foreman. The collection of distal flows is not Borel. American journal of mathematics, vol. 117 (1995), pp. 203–239. - Ferenc Beleznay and Matthew Foreman. The complexity of the collection of measure-distal transformations. Ergodic theory and dynamical systems, vol. 16 (1996), pp. 929–962. - Howard Becker. Pointwise limits of subsequences and sets. Fundamenta mathematicae, vol. 128 (1987), pp. 159–170. - Howard Becker, Sylvain Kahane, and Alain Louveau. Some complete sets in harmonic analysis. Transactions of the American Mathematical Society, vol. 339 (1993), pp. 323–336. - Robert Kaufman. PCA sets and convexity Fundamenta mathematicae, vol. 163 (2000), pp. 267–275). - Howard Becker. Descriptive set theoretic phenomena in analysis and topology. Set theory of the continuum, edited by H. Judah, W. Just, and H. Woodin, Mathematical Sciences Research Institute publications, vol. 26, Springer-Verlag, New York, Berlin, Heidelberg, etc., 1992, pp. 1–25.

2001 ◽  
Vol 7 (3) ◽  
pp. 385-388
Author(s):  
Gabriel Debs
Keyword(s):  
New York ◽  
Dynamical Systems ◽  
Harmonic Analysis ◽  
Ergodic Theory ◽  
Set Theory ◽  
American Mathematical Society ◽  
And Topology ◽  
Mathematical Sciences ◽  
Descriptive Set ◽  
The Continuum

scholarly journals Category Theory for Autonomous and Networked Dynamical Systems

Entropy ◽  
2019 ◽  
Vol 21 (3) ◽  
pp. 302 ◽  
Author(s):  
Jean-Charles Delvenne
Keyword(s):  
Dynamical Systems ◽  
Systems Theory ◽  
Ergodic Theory ◽  
Category Theory ◽  
Open Systems ◽  
Topological Dynamics ◽  
Control Problems ◽  
Natural Conditions ◽  
Discussion Paper ◽  
Open Systems Theory

In this discussion paper we argue that category theory may play a useful role in formulating, and perhaps proving, results in ergodic theory, topogical dynamics and open systems theory (control theory). As examples, we show how to characterize Kolmogorov–Sinai, Shannon entropy and topological entropy as the unique functors to the nonnegative reals satisfying some natural conditions. We also provide a purely categorical proof of the existence of the maximal equicontinuous factor in topological dynamics. We then show how to define open systems (that can interact with their environment), interconnect them, and define control problems for them in a unified way.

Ergodic Theory in Statistical Mechanics

Physics Today ◽  
1966 ◽  
Vol 19 (6) ◽  
pp. 91-92
Author(s):  
I. E. Farquhar ◽  
R. B. Lindsay
Keyword(s):  
Statistical Mechanics ◽  
Ergodic Theory

scholarly journals Introduction to Focus Issue: Statistical mechanics and billiard-type dynamical systems

2012 ◽  
Vol 22 (2) ◽  
pp. 026101 ◽  
Author(s):  
Edson D. Leonel ◽  
Marcus W. Beims ◽  
Leonid A. Bunimovich
Keyword(s):  
Dynamical Systems ◽  
Statistical Mechanics

Erratum to ‘Semi-hyperbolic fibered rational maps and rational semigroups’ (Ergodic Theory and Dynamical Systems 26 (2006), 893–922)

2008 ◽  
Vol 28 (3) ◽  
pp. 1043-1045 ◽  
Author(s):  
HIROKI SUMI
Keyword(s):  
Dynamical Systems ◽  
Ergodic Theory ◽  
Rational Maps

AbstractWe give a correction to the assumption of Theorems 1.12 and 2.6 in the paper [H. Sumi. Semi-hyperbolic fibered rational maps and rational semigroups. Ergod. Th. & Dynam. Sys.26 (2006), 893–922].

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