Bers and Hénon, Painlevé and Schroedinger

Abstract

We study the dynamics of mapping class groups on 2-dimensional character varieties. We shall show that the dynamics of pseudo-Anosov mapping classes resembles in many ways the dynamics of Hénon mappings, and then apply this idea to answer open questions concerning the geometry of discrete and faithful representations, Painlevé sixth equation, and discrete Schroedinger operators.

References in corpus (1)

• Hyperbolicity of the Trace Map for the Weakly Coupled Fibonacci Hamiltonian

Cited by in corpus (19)

• Schrödinger Operators with Dynamically Defined Potentials: A Survey
• The Fibonacci Hamiltonian
• Spectral and Quantum Dynamical Properties of the Weakly Coupled Fibonacci Hamiltonian
• Hyperbolicity of the Trace Map for the Weakly Coupled Fibonacci Hamiltonian
• Absolutely Continuous Convolutions of Singular Measures and an Application to the Square Fibonacci Hamiltonian
• On stochastic sea of the standard map
• Spectra of Discrete Schrödinger Operators with Primitive Invertible Substitution Potentials
• The fractal dimensions of the spectrum of Sturm Hamiltonian
• Continuum Schrödinger Operators Associated With Aperiodic Subshifts
• Quantum and Spectral Properties of the Labyrinth Model
• Dynamical Green Functions and Discrete Schrödinger Operators with Potentials Generated by Primitive Invertible Substitution
• Hölder Continuity of the Integrated Density of States for the Fibonacci Hamiltonian
• On the Hausdorff dimension of the spectrum of Thue-Morse Hamiltonian
• The spectral properties of the strongly coupled Sturm Hamiltonian of eventually constant type
• The spectrum of period-doubling Hamiltonian
• The Spectrum and the Spectral Type of the Off-Diagonal Fibonacci Operator
• The dynamical degree of billiards in an algebraic curve
• The spectral characteristics of the Sturm Hamiltonian with eventually periodic type
• The Spectrum of the Weakly Coupled Fibonacci Hamiltonian