2005/05/03 by Eric Bedford, Bedford, Eric, Jeffrey Diller +1
Mathematics · Physics and Astronomy · #32H50 (secondary) #37F20 (primary) #Advanced Differential Equations and Dynamical Systems #Complex Variables (math.CV) #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Dynamics and Fractals #Quantum chaos and dynamical systems #math.CV #math.DS #msc:32H50 #msc:37F20
paper · pdf · doi:10.48550/arxiv.math/0505062
23 pages, 18 figures
arxiv created 2005/05/03 · openalex publication_date 2005/05/03 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We consider the real dynamics of a two parameter family of plane birational maps, focusing especially on an open subset of parameter space on which the real and complex dynamics are in close agreement. On the complex side, we find a rational complex surface to which the maps extend in a well-defined fashion and then calculate the induced action on the Picard group of the surface. On the real side, we use the critical sets of the maps to produce a combinatorial model for the dynamics. By comparing the two points of view, we are able to code points in the real non-wandering set, describe the behavior of wandering orbits, and identify a measure of maximal entropy for the real dynamics.