Normal forms and Misiurewicz renormalization for dissipative surface diffeomorphisms

2014/04/08 by Pierre Berger, Berger, Pierre
Mathematics · Physics and Astronomy · #Chaos control and synchronization #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Dynamics and Fractals #Quantum chaos and dynamical systems #math.DS

paper · pdf · doi:10.48550/arxiv.1404.2235

arxiv created 2014/04/08 · openalex publication_date 2014/04/08 · arxiv updated 2014/04/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We define a hyperbolic renormalizations suitable for maps of small determinant, with uniform bounds for large periods. The techniques involve an improvement of the celebrated Palis-Takens renormalization and normal forms (fibered linearizations). These techniques are useful to study the dynamics of Hénon like maps and the geometry of their parameter space.

Citations

• Parabolic Bifurcations in Complex Dimension 2
• Abundance of non-uniformly hyperbolic Hénon like endomorphisms
• Statistical properties of unimodal maps: smooth families with negative Schwarzian derivative
• Remarks on iterated cubic maps
• Deterministic Nonperiodic Flow

Related

• Strongly dissipative surface diffeomorphisms
• Renormalization of Hénon map in arbitrary dimension I : Universality and reduction of ambient space
• Renormalization in the Golden-Mean Semi-Siegel Hénon Family: Universality and Non-Rigidity
• On Regular Hénon-like Renormalization
• Spectral properties of renormalization for area-preserving maps