Mathematische Zeitschrift

, Volume 291, Issue 3–4, pp 1543–1568 | Cite as

Attracting graphs of skew products with non-contracting fiber maps

  • Lorenzo J. DíazEmail author
  • Edgar Matias


We study attracting graphs of step skew products from the topological and ergodic points of view where the usual contracting-like assumptions of the fiber dynamics are replaced by weaker merely topological conditions. In this context, we prove the existence of an attracting invariant graph and study its topological properties. We prove the existence of globally attracting measures and we show that (in some specific cases) the rate of convergence to these measures is exponential.


Attracting measure Bony set Coding map Invariant graph Skew product Target set 

Mathematics Subject Classification

37C70 58F12 37A30 


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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Departamento de Matemática PUC-RioRio de JaneiroBrazil
  2. 2.Instituto de Matemática Universidade Federal do Rio de JaneiroRio de JaneiroBrazil
  3. 3.Departamento de MatemáticaICMC-USPSão Carlos-SPBrazil

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