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Ergodic theory

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. The notion of deterministic…

History, Examples & Ergodic flows on manifolds

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Overview

Ergodic transformations

Examples

Ergodic theorems

Probabilistic formulation: Birkhoff–Khinchin theorem

Mean ergodic theorem

Convergence of the ergodic means in the Lp norms

Sojourn time

Ergodic flows on manifolds

Historical references

Modern references

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Ergodic theory

Nodes143
Edges142
Triples103
Avg. degree1.99
Density0.013986
Components1

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Ergodic theory

Top relations

related to Modern references · 87
Ergodic theory → Addison, Advanced Mathematics, Alexandria Conference, An, Andrzej Lasota, André Avez, Anosov, Applications, Applied Mathematics, Benjamin, Birkhoff, Bourgain, Cambridge, Cambridge Studies, Cambridge University Press, Caroline, Chaos, Classical Mechanics, Connections, Cours
see also · 7
Ergodic theory → Bogolyubov, Bowen, Ergodic, K-SystemsBernoulli, Krylov, Ruelle, Wintner
related to External links · 4
Ergodic theory → Cosma Rohilla ShaliziErgodic, From Physics World, June, Notes
related to Ergodic transformations · 3
Ergodic theory → At, Ergodic, The
is a · 2
Ergodic theory → behavior of a dynamical system when it is allowed to run for a long time, branch of mathematics that studies statistical properties of deterministic dynamical systems

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Important terminology

ergodic theory theorem space time measure systems ergodicity dynamical average properties displaystyle almost theorems applications set system birkhoff mathematics doi

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Ergodic theoryis abranch of mathematics that studies statistical properties of deterministic dynamical systems0.90text
Ergodic theoryis abehavior of a dynamical system when it is allowed to run for a long time0.90text
Ergodic theoryrelated to Ergodic transformationsErgodic0.60section
Ergodic theoryrelated to Ergodic transformationsThe0.60section
Ergodic theoryrelated to Ergodic transformationsAt0.60section
Ergodic theoryrelated to External linksJune0.60section
Ergodic theoryrelated to External linksNotes0.60section
Ergodic theoryrelated to External linksCosma Rohilla ShaliziErgodic0.60section
Ergodic theoryrelated to External linksFrom Physics World0.60section
Ergodic theoryrelated to Modern referencesAnosov0.60section
Ergodic theoryrelated to Modern referencesErgodic0.60section
Ergodic theoryrelated to Modern referencesEncyclopedia0.60section

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