Details

Autor(en) / Beteiligte

• DOWNAROWICZ, T.

Titel

Positive topological entropy implies chaos DC2

Ist Teil von

• Proceedings of the American Mathematical Society, 2014-01, Vol.142 (1), p.137-149

Ort / Verlag

AMERICAN MATHEMATICAL SOCIETY

Erscheinungsjahr

2014

Quelle

Free E-Journal (出版社公開部分のみ）

Beschreibungen/Notizen

• Using methods of entropy in ergodic theory, we prove that positive topological entropy implies chaos DC2. That is, if a system (X, T) has positive topological entropy, then there exists an uncountable set E such that for any two distinct points x, y in E, $\begin{matrix} lim inf \ \\ n\rightarrow \infty \ \end{matrix} \frac {1}{n}\sum_{i=1}^{n} dist (T ^i x, T^i y)=0$ and $\begin{matrix} lim sup \ \\ n\rightarrow \infty \ \end{matrix} \frac {1}{n}\sum_{i=1}^{n} dist (T ^i x, T^i y)> 0$.