Statements (40)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
Mathematical discipline
|
| gptkbp:appliesTo |
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 |
| https://www.w3.org/2000/01/rdf-schema#label |
Ergodic Theory
|
| 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
|