Length-expanding Lipschitz maps on totally regular continua

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:412

Article

Spitalsky, Vladimir

关键词: Lipschitz map;    Length-expanding map;    Tent map;    Totally regular continuum;    Rectifiable curve;    Exact Devaney chaos;    Specification property;   

DOI  :  10.1016/j.jmaa.2013.10.017

来源: Elsevier

【 摘 要 】

The tent map is an elementary example of an interval map possessing many interesting properties, such as dense periodicity, exactness, Lipschitzness and a kind of length-expansiveness. It is often used in constructions of dynamical systems on the interval/trees/graphs. The purpose of the present paper is to construct, on totally regular continua (i.e. on topologically rectifiable curves), maps sharing some typical properties with the tent map. These maps will be called length-expanding Lipschitz maps, briefly LEL maps. We show that every totally regular continuum endowed with a-suitable metric admits a LEL map. As an application we obtain that every non-degenerate totally regular continuum admits an exactly Devaney chaotic map with finite entropy and the specification property. (C) 2013 Elsevier Inc. All rights reserved.

【 授权许可】

Free