A continuous bowen-mañé type phenomenon

Esteban Muñoz-Young, Andrés Navas, Enrique Pujals, Carlos H. Vásquez

Research output: Contribution to journalArticlepeer-review

2 Scopus citations

Abstract

In this work we exhibit a one-parameter family of C1- diffeomorphisms Fα of the 2-sphere, where α > 1, such that the equator S1 is an attracting set for every F α and Fα|S1 is the identity. For α > 2 the Lebesgue measure on the equator is a non ergodic physical measure having uncountably many ergodic components. On the other hand, for 1 < α < 2 there is no physical measure for Fα. If α < 2 this follows directly from the fact that the ω-limit of almost every point is a single point on the equator (and the basin of each of these points has zero Lebesgue measure). This is no longer true for α = 2, and the non existence of physical measure in this critical case is a more subtle issue.

Original languageEnglish
Pages (from-to)713-724
Number of pages12
JournalDiscrete and Continuous Dynamical Systems
Volume20
Issue number3
DOIs
StatePublished - Mar 2008
Externally publishedYes

Keywords

  • Ergodic components
  • Physical measures

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