The selecting Lemma of Liao

Pages: 159 - 175, Volume 20, Issue 1, January 2008

doi:10.3934/dcds.2008.20.159       Abstract        Full Text (215.6K)       Related Articles

Lan Wen - School of Mathematic Sciences, Peking University, Beijing, 100871, China (email)

Abstract: The selecting lemma of Liao selects, under certain conditions of a non-hyperbolic setting, a special kind of orbits of finite length, called quasi-hyperbolic strings, which can be shadowed by true orbits. In this article we give an exposition on this lemma, and illustrate some recent applications.

Keywords:  selecting, quasi-hyperbolic string, dominated splitting, shadowing.
Mathematics Subject Classification:  37D30.

Received: February 2007;      Revised: August 2007;      Published: October 2007.