Boletim da Sociedade Brasileira de Matemática - Bulletin/Brazilian Mathematical Society

, Volume 28, Issue 2, pp 271–314

Ergodic properties of Anosov maps with rectangular holes

  • N. Chernov
  • R. Markarian

DOI: 10.1007/BF01233395

Cite this article as:
Chernov, N. & Markarian, R. Bol. Soc. Bras. Mat (1997) 28: 271. doi:10.1007/BF01233395


We study Anosov diffeomorphisms on manifolds in which some ‘holes’ are cut. The points that are mapped into those holes disappear and never return. The holes studied here are rectangles of a Markov partition. Such maps generalize Smale's horseshoes and certain open billiards. The set of nonwandering points of a map of this kind is a Cantor-like set calledrepeller. We construct invariant and conditionally invariant measures on the sets of nonwandering points. Then we establish ergodic, statistical, and fractal properties of those measures.

Copyright information

© Sociedade Brasileira de Matemática 1997

Authors and Affiliations

  • N. Chernov
    • 1
  • R. Markarian
    • 2
  1. 1.Department of MathematicsUniversity of Alabama in BirminghamBirminghamUSA
  2. 2.Instituto de Matemática y Estadística “Prof. Ing. Rafael Laguardia”Facultad de Ingenieríanewline Universidad de la RepúblicaMontevideoUruguay