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Erschienen in:
2004 | OriginalPaper | Buchkapitel
Ergodicity and Ergodic Points
verfasst von : Giovanni Gallavotti, Federico Bonetto, Guido Gentile
Erschienen in: Aspects of Ergodic, Qualitative and Statistical Theory of Motion
Verlag: Springer Berlin Heidelberg
Enthalten in: Professional Book Archive
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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 ⊂ ℝ2r and Ω = W, cf. definition 1.3.1. This means looking at motions observed at time intervals t0. More precisely the following proposition holds.