Periodicities in Linear Fractional Recurrences: Degree growth of birational surface maps

2005/09/27 by Eric Bedford, Bedford, Eric, Kyounghee Kim +1 · 1 citation
Mathematics · Medicine · #32M99 #37F99 #Advanced Differential Equations and Dynamical Systems #Complex Variables (math.CV) #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Dynamics and Fractals #Mathematical and Theoretical Epidemiology and Ecology Models #math.CV #math.DS #msc:32M99 #msc:37F99

paper · pdf · doi:10.48550/arxiv.math/0509645

arxiv created 2005/09/27 · openalex publication_date 2005/09/27 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider the set of all 2-step recurrences (difference equations) that are given by linear fractional maps. These give birational maps of the plane. We determine the degree growth of these birational maps. We find the all the maps in this family that are periodic. This also leads to new surface automorphisms with positive entropy.

Citations

• Energy and Invariant Measures for Birational Surface Maps

Cited by

• Real Rational Surface Automorphisms : Positivity and Linearity

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