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gptkbp:instanceOf
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gptkb:Mathematical_discipline
|
|
gptkbp:appliesTo
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gptkb:Hamiltonian_systems
Markov processes
Random walks
|
|
gptkbp:field
|
gptkb:Mathematics
|
|
gptkbp:hasApplication
|
Analysis of large systems
Mathematical modeling of complex systems
Randomness in deterministic systems
Statistical properties of physical systems
Time averages and space averages equivalence
|
|
gptkbp:hasConcept
|
Mixing
Recurrence
Ergodic decomposition
Ergodic transformation
|
|
gptkbp:notablePerson
|
gptkb:George_David_Birkhoff
gptkb:John_von_Neumann
gptkb:Eberhard_Hopf
gptkb:Vladimir_Arnold
gptkb:Andrey_Kolmogorov
gptkb:Ya._G._Sinai
|
|
gptkbp:originatedIn
|
Late 19th century
|
|
gptkbp:relatedTo
|
gptkb:Statistical_mechanics
gptkb:Probability_theory
Functional analysis
Measure theory
Topological dynamics
|
|
gptkbp:studies
|
Dynamical systems
Invariant measures
Long-term average behavior
|
|
gptkbp:theory
|
Birkhoff Ergodic Theorem
Poincaré Recurrence Theorem
von Neumann Ergodic Theorem
|
|
gptkbp:usedIn
|
gptkb:Number_theory
gptkb:Thermodynamics
gptkb:Quantum_mechanics
gptkb:Chaos_theory
Information theory
|
|
gptkbp:bfsParent
|
gptkb:Graduate_Studies_in_Mathematics
|
|
gptkbp:bfsLayer
|
7
|
|
https://www.w3.org/2000/01/rdf-schema#label
|
Ergodic Theory
|