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Porcupine-Like Horseshoes: Topological and Ergodic Aspects

  • L. J. DíazEmail author
  • K. Gelfert
Conference paper
Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 54)

Abstract

We introduce a class of topologically transitive and partially hyperbolic sets called porcupine-like horseshoes. The dynamics of these sets is a step skew product over a horseshoe. The fiber dynamics is given by a one-dimensional genuinely noncontracting iterated function system. We study this dynamics and explain how the properties of the iterated function system can be translated to topological and ergodic properties of the porcupines.

Keywords

Lyapunov Exponent Periodic Point Invariant Manifold Unstable Manifold Iterate Function System 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Notes

Acknowledgements

This paper was partially supported by CNPq (research grants and Projeto Universal), CNE Faperj, and Pronex (Brazil) and Balzan Research Project of J. Palis.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  1. 1.Departamento de MatemáticaPUC-RioRio de JaneiroBrazil
  2. 2.Instituto de MatemáticaUniversidade Federal do Rio de JaneiroRio de JaneiroBrazil

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