Ergodicity and Ergodic Points

Abstract

The problem of determining which sets are visited with defined frequency by the motions of a dynamical system (Ω, S) can be satisfactorily solved in the case of particularly simple systems; for instance in the case in which $S = {S_{{t_0}}}$ and (S _t )_t∈ℝ is a Hamiltonian flow which is analytically integrable on a region W ⊂ ℝ^2r and Ω = W, cf. definition 1.3.1. This means looking at motions observed at time intervals t ₀. More precisely the following proposition holds.