, Volume 16, Issue 3, pp 409-430

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

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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.

Communicated by John Eric Fornæss