Infinite-modal maps with global chaotic behavior
type: Item
instance of: scholarly article
title: Infinite-modal maps with global chaotic behavior
zbMATH Open document ID: 0916.58029
DOI: 10.2307/121002
published in: Annals of Mathematics. Second Series
publication date: 1999-06-16T00:00:00Z
full work available at URL: 148 2.html
review text: The main goal is to study the dynamics of certain parametrized families \((f_\mu)_\mu\) of one-dimensional maps with infinite critical set. The authors show that they exhibit global chaotic behaviour in a persistent way: For a positive Lebesgue measure set of parameter values the map is transitive and almost every orbit has positive Lyapunov exponent. This class of systems is motivated by a problem in the dynamics of flows in three dimensions: the unfolding of saddle-focus homoclinic connections.
Mathematics Subject Classification ID: 37D45
zbMATH DE Number: 1267996
zbMATH Keywords: critical set
zbMATH Keywords: chaotic behaviour
zbMATH Keywords: homoclinic connections
zbMATH Keywords: saddle-focus homoclinic connections
author: M. J. Pacifico
author: A. Rovella
author: Marcelo Viana
reviewed by: Messoud Efendiev
MaRDI profile type: Publication
OpenAlex ID: W2011814687
description: scientific article; zbMATH DE number 1267996