Existence of unique SRB-measures is typical for real unicritical polynomial families

DOI10.1016/j.ansens.2006.02.001zbMath1112.37018OpenAlexW2003410587WikidataQ59184860 ScholiaQ59184860MaRDI QIDQ3413470

Henk Bruin, Wei Xiao Shen, Sebastian J. van Strien

Publication date: 7 December 2006

Published in: Annales Scientifiques de l’École Normale Supérieure (Search for Journal in Brave)

Full work available at URL: http://www.numdam.org/item?id=ASENS_2006_4_39_3_381_0

zbMATH Keywords

SRB-measuresCantor attractormetric attractorsfamilies of real unicritical polynomial mapsuniquely ergodic dynamical systems

Mathematics Subject Classification ID

Smooth ergodic theory, invariant measures for smooth dynamical systems (37C40) Strange attractors, chaotic dynamics of systems with hyperbolic behavior (37D45) Dynamical systems involving maps of the interval (37E05)

Related Items (10)

The topological complexity of Cantor attractors for unimodal interval maps ⋮ The dynamics of complex box mappings ⋮ Complex bounds for real maps ⋮ Parapuzzle of the Multibrot set and typical dynamics of unimodal maps ⋮ Hausdorff dimension of Cantor attractors in one-dimensional dynamics ⋮ On the Lebesgue measure of Li-Yorke pairs for interval maps ⋮ Renormalization of symmetric bimodal maps with low smoothness ⋮ On the finiteness of attractors for piecewise maps of the interval ⋮ Describing the dynamics and complexity of Matsumoto-Nonaka's duopoly model ⋮ Proof of the Branner-Hubbard conjecture on Cantor Julia sets

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Feigenbaum-Coullet-Tresser universality and Milnor's hairiness conjecture
• Invariant measures exist without a growth condition
• Regular or stochastic dynamics in real analytic families of unimodal maps
• Invariant measures exist under a summability condition for unimodal maps
• Combinatorics, geometry and attractors of quasi-quadratic maps
• Almost every real quadratic map is either regular or stochastic.
• Wild Cantor attractors exist
• Statistical properties of unimodal maps: The quadratic family
• Rigidity for real polynomials
• Density of hyperbolicity in dimension one
• Decay of geometry for unimodal maps: an elementary proof
• Extensions of Jentzsch's Theorem
• On the dynamics of polynomial-like mappings
• Holomorphic Motions and Polynomial Hulls
• Measurable dynamics of $S$-unimodal maps of the interval
• Distortion results and invariant Cantor sets of unimodal maps
• Topological conditions for the existence of absorbing Cantor sets
• Minimal Cantor Systems and Unimodal Maps
• Decay of correlations in one-dimensional dynamics
• Linearly recurrent subshifts have a finite number of non-periodic subshift factors
• Induced expansion for quadratic polynomials
• Real bounds, ergodicity and negative Schwarzian for multimodal maps
• Complex Dynamics and Renormalization (AM-135)
• Getting rid of the negative Schwarzian derivative condition

This page was built for publication: Existence of unique SRB-measures is typical for real unicritical polynomial families