Renormalisable Henon-like Maps and Unbounded Geometry

2010/02/22 by Peter Hazard, Hazard, Peter, Mikhail Lyubich +3
Mathematics · Physics and Astronomy · #Advanced Differential Equations and Dynamical Systems #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Dynamics and Fractals #Quantum chaos and dynamical systems

paper · pdf · doi:10.48550/arxiv.1002.3942

openalex publication_date 2010/02/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We show that given a one parameter family F_b of strongly dissipative infinitely renormalisable Hénon-like maps, parametrised by a quantity called the `average Jacobian' b, the set of all parameters b such that F_b has a Cantor set with unbounded geometry has full Lebesgue measure.

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