Non-uniformly expanding dynamics in maps with singularities and criticalities

Stefano Luzzatto, Warwick Tucker

Research output: Contribution to journalArticleResearchpeer-review

21 Citations (Scopus)

Abstract

We investigate a one-parameter family of interval maps arising in the study of the geometric Lorenz flow for non-classical parameter values. Our conclusion is that for all parameters in a set of positive Lebesgue measure the map has a positive Lyapunov exponent. Furthermore, this set of parameters has a density point which plays an important dynamic role. The presence of both singular and critical points introduces interesting dynamics, which have not yet been fully understood.

Original languageEnglish
Pages (from-to)179-226
Number of pages48
JournalPublications Mathématiques de l'IHÉS
Volume89
Issue number1
DOIs
Publication statusPublished - 1 Dec 1999
Externally publishedYes

Cite this