Expansivity and Cone-fields in Metric Spaces

被引：2

作者：

Struski, Lukasz ^{[1
]}

Tabor, Jacek ^{[1
]}

机构：

[1] Jagiellonian Univ, Fac Math & Comp Sci, Lojasiewicza 6, PL-30348 Krakow, Poland

来源：

JOURNAL OF DYNAMICS AND DIFFERENTIAL EQUATIONS | 2014年 / 26卷 / 03期

关键词：

Cone-field; Hyperbolicity; Expansive map; Lyapunov function; LYAPUNOV FUNCTIONS;

D O I：

10.1007/s10884-014-9373-2

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Due to the results of Lewowicz and Tolosa expansivity can be characterized with the aid of Lyapunov function. In this paper we study a similar problem for uniform expansivity and show that it can be described using generalized cone-fields on metric spaces. We say that a function is uniformly expansive on a set if there exist and such that for any two orbits , of we have It occurs that a function is uniformly expansive iff there exists a generalized cone-field on such that is cone-hyperbolic.

引用

页码：517 / 527

页数：11

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