Details

Autor(en) / Beteiligte

• Mai, Jie-Hua

Titel

Devaney's chaos implies existence of s-scrambled sets

Ist Teil von

• Proceedings of the American Mathematical Society, 2004-09, Vol.132 (9), p.2761-2767

Ort / Verlag

Providence, RI: American Mathematical Society

Erscheinungsjahr

2004

Link zum Volltext

Quelle

American Mathematical Society Publications

Beschreibungen/Notizen

• Let X be a complete metric space without isolated points, and let f:X\to X be a continuous map. In this paper we prove that if f is transitive and has a periodic point of period p, then f has a scrambled set S=\bigcup _{n=1}^{\infty }C_{n} consisting of transitive points such that each C_{n} is a synchronously proximal Cantor set, and \bigcup _{i=0}^{p-1}f^{i}(S) is dense in X. Furthermore, if f is sensitive (for example, if f is chaotic in the sense of Devaney), with 2s being a sensitivity constant, then this S is an s-scrambled set.