The Journal of Geometric Analysis

, 16:409

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

Authors

  • Eric Bedford
    • Indiana University Bloomington
    • University of Notre Dame Notre Dame
  • Jeff Diller
    • Indiana University Bloomington
    • University of Notre Dame Notre Dame
Article

DOI: 10.1007/BF02922060

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

Abstract

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

32H5014E0737D5037F20

Key Words and Phrases

Birational mapMarkov partitioninvariant measure

Copyright information

© Mathematica Josephina, Inc. 2006