The Henon Family: The Complex Horseshoe Locus and Real Parameter Space

2005/01/26 by Eric Bedford, Bedford, Eric, John Smillie +1
Computer Science · Mathematics · #Geometric and Algebraic Topology #Mathematical Dynamics and Fractals #Topological and Geometric Data Analysis #math.CV #math.DS

paper · pdf · doi:10.48550/arxiv.math/0501475

arxiv created 2005/01/26 · arxiv updated 2009/12/01

Abstract

We consider the complexification of the Henon family of quadratic diffeomorphisms of the plane, and the region of parameter space corresponding to complex horseshoes. We discuss some conjectures about the global topology of the complex horseshoe locus.

Related

• Complex Horseshoes and the Dynamics of Mappings of Two Complex Variables
• Boundary of the horseshoe locus for the Hénon family
• Real Polynomial Diffeomorphisms with Maximal Entropy: II. Small Jacobian
• Critical locus for Hénon maps in an HOV region
• On parameter loci of the Hénon family