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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#에르고딕#ergodic#동역학#dynamics