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Ergodic theory is a branch of mathematics that studies statistical properties of deterministic dynamical systems; it is the study of ergodicity. In this context, "statistical properties" refers to properties which are expressed through the behavior of time averages of various functions along trajectories of dynamical systems.
Die Ergodentheorie ist ein Teilgebiet der Mathematik, das sowohl der Maßtheorie und Stochastik als auch der Theorie dynamischer Systeme zugeordnet wird. Die Ursprünge der Ergodentheorie liegen in der statistischen Physik.
These are notes from a course on ergodic theory taught by Maryam Mirzakhani at Stanford in 2014. They cover topics such as spectral invariants, entropy, mixing, pointwise ergodic theorems, and topological dynamics.
Ergodizität (griechisch έργον: Werk und όδος: Weg) eines dynamischen Systems benennt die Eigenschaft, dass während der zeitlichen Entwicklung des Systems alle physikalisch möglichen Zustände auch wirklich erreicht werden.
1. Aug. 2023 · A comprehensive overview of ergodic theory and its applications, covering classical and recent developments, connections, and topics. Edited by Cesar E. Silva and Alexandre I. Danilenko, with contributions from experts in the field.
What is ergodic theory? Ergodic theory is the theory of dynamical systems, i.e., of measure preserving actions of groups or monoids on probability spaces. Such systems often occur in models of real-world phenomena. But also in theoretical mathematics, dynamical systems have a wide range of applications. In this course, we will introduce the ...
3. Feb. 2023 · Ergodic theory is a branch of mathematics that studies the statistical properties of dynamical systems using measure-theoretic and probabilistic tools. This article provides an overview of the history, topics, and applications of ergodic theory, as well as references to original articles and surveys.
