Ergodic Theory
★★★★★Graduate+
📖Definition
Study of long-term average behavior of dynamical systems. Time average = Space average
📐Formulas
lim (1/n)Σf(Tⁱx) = ∫f dμ (a.e.)
Ergodic: invariant sets trivial
Mixing: correlations decay
✏️Examples
예제 1
Rotation
예제 2
Bernoulli shift
예제 3
Baker's map
⚡Applications
Statistical mechanics
Number theory
Chaos
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