Non-periodic bifurcations of one-dimensional maps
Carregando...
Fontes externas
Fontes externas
Data
Orientador
Coorientador
Pós-graduação
Curso de graduação
Título da Revista
ISSN da Revista
Título de Volume
Editor
Cambridge University Press
Cambridge University Press (CUP)
Cambridge University Press (CUP)
Tipo
Artigo
Direito de acesso
Acesso aberto
Fontes externas
Fontes externas
Resumo
We prove that a 'positive probability' subset of the boundary of '{uniformly expanding circle transformations}' consists of Kupka-Smale maps. More precisely, we construct an open class of two-parameter families of circle maps (f(alpha,theta))(alpha,theta) such that, for a positive Lebesgue measure subset of values of alpha, the family (f(alpha,theta))(theta) crosses the boundary of the uniformly expanding domain at a map for which all periodic points are hyperbolic (expanding) and no critical point is pre-periodic. Furthermore, these maps admit an absolutely continuous invariant measure. We also provide information about the geometry of the boundary of the set of hyperbolic maps.
Descrição
Palavras-chave
Idioma
Inglês
Citação
Ergodic Theory and Dynamical Systems. New York: Cambridge Univ Press, v. 27, p. 459-492, 2007.
