The Journal of Geometric Analysis

, 16:409

Dynamics of a two parameter family of plane birational maps: Maximal entropy

  • Eric Bedford
  • Jeff Diller

DOI: 10.1007/BF02922060

Cite this article as:
Bedford, E. & Diller, J. J Geom Anal (2006) 16: 409. doi:10.1007/BF02922060


We mix combinatorial with complex methods to study the dynamics of a real two parameter family of plane birational maps. Specifically, we consider the action of the maps on the Picard group of an appropriate compactification of the complex plane, on the homology groups of a forward invariant real subset of this compactification, and on a Markov partition of the real plane determined by the critical set. For the range of parameters considered, the three actions are equivalent. This allows us to construct a measure of maximal entropy on the real nonwandering set, and it allows us to show that all wandering points are attracted to infinity in a well-defined fashion.

Math Subject Classifications

32H50 14E07 37D50 37F20 

Key Words and Phrases

Birational map Markov partition invariant measure 

Copyright information

© Mathematica Josephina, Inc. 2006

Authors and Affiliations

  • Eric Bedford
    • 1
    • 2
  • Jeff Diller
    • 1
    • 2
  1. 1.Indiana University Bloomington
  2. 2.University of Notre Dame Notre Dame

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