Families, filters and chaos | Zendy

Oprocha Piotr | Zendy

AI Assistant Blog Pricing

Home ZAIA Blog

Premium

Families, filters and chaos

Author(s) -

Oprocha Piotr

Publication year - 2010

Publication title -

bulletin of the london mathematical society

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 2.396

H-Index - 48

eISSN - 1469-2120

pISSN - 0024-6093

DOI - 10.1112/blms/bdq034

Subject(s) - mathematics , topological entropy , mixing (physics) , chaos (operating system) , compact space , metric space , set (abstract data type) , sequence (biology) , topological conjugacy , entropy (arrow of time) , pure mathematics , metric (unit) , topological space , topology (electrical circuits) , discrete mathematics , combinatorics , computer science , physics , computer security , quantum mechanics , biology , genetics , programming language , operations management , economics

In this paper, we use the definition of ( ℱ 1 , ℱ 2 )‐chaos introduced recently by Tan and Xiong together with the properties of residual relations as a tool in construction of various kinds of scrambled sets. In particular, we show that a continuous map acting on a compact metric space has an ε ‐scrambled set if and only if it has a distributionally ε ‐scrambled set with respect to a sequence. We also provide an example of a topologically mixing map with positive topological entropy but without DC1 pairs.

This content is not available in your region!

Continue researching here.

Having issues? You can contact us here

Accelerating Research