Real polynomial diffeomorphisms with maximal entropy: II. Small Jacobian

DOI10.1017/S0143385706000095zbMath1135.37015arXivmath/0402355MaRDI QIDQ3419194

John Smillie, Eric Bedford

Publication date: 6 February 2007

Published in: Ergodic Theory and Dynamical Systems (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0402355

zbMATH Keywords

horseshoetopological conjugacytopological entropystable and unstable manifoldshomoclinic tangencyheteroclinic tangencyHénon diffeomorphisms

Mathematics Subject Classification ID

Topological entropy (37B40) Dynamical systems involving homeomorphisms and diffeomorphisms of planes and surfaces (37E30) Homoclinic and heteroclinic orbits for dynamical systems (37C29) Bifurcations connected with nontransversal intersection in dynamical systems (37G25) Dynamical systems involving smooth mappings and diffeomorphisms (37C05)

Related Items (19)

Skew product cycles with rich dynamics: From totally non-hyperbolic dynamics to fully prevalent hyperbolicity ⋮ Birkhoff spectrum for Hénon-like maps at the first bifurcation ⋮ Removal of phase transition in the Chebyshev quadratic and thermodynamics for Hénon-like maps near the first bifurcation ⋮ Global dynamics of quadratic second order difference equation in the first quadrant ⋮ Dynamics of polynomial diffeomorphisms of \(\mathbb {C}^2\): combinatorial and topological aspects ⋮ On parameter loci of the Hénon family ⋮ Hyperbolic invariant sets of the real generalized Hénon maps ⋮ Prevalent dynamics at the first bifurcation of Hénon-like families ⋮ A symbolic characterization of the horseshoe locus in the Hénon family ⋮ The boundary of hyperbolicity for Hénon-like families ⋮ Characterization of Dynamics of a Class of Polynomial Automorphisms in ℂn ⋮ Lyapunov spectrum for Hénon-like maps at the first bifurcation ⋮ Equilibrium Measures at Temperature Zero for Hénon-Like Maps at the First Bifurcation ⋮ Boundary of the Horseshoe Locus for the Hénon Family ⋮ Equilibrium measures for the Hénon map at the first bifurcation: uniqueness and geometric/statistical properties ⋮ Destroying horseshoes via heterodimensional cycles: generating bifurcations inside homoclinic classes ⋮ Chaotic Polynomial Maps ⋮ Thermodynamics of towers of hyperbolic type ⋮ On the dynamics near infinity of some polynomial mappings in \(\mathbb C^2\)

This page was built for publication: Real polynomial diffeomorphisms with maximal entropy: II. Small Jacobian