Critical covering maps without absolutely continuous invariant probability measure

DOI10.3934/dcds.2019101zbMath1408.37069OpenAlexW2909972714WikidataQ128530903 ScholiaQ128530903MaRDI QIDQ1735342

Xianqiang Yang

Publication date: 28 March 2019

Published in: Discrete and Continuous Dynamical Systems (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.3934/dcds.2019101

zbMATH Keywords

ergodicitykneading mapArnold family

Mathematics Subject Classification ID

Dynamical aspects of measure-preserving transformations (37A05) Dynamical systems involving maps of the circle (37E10) Smooth ergodic theory, invariant measures for smooth dynamical systems (37C40) Combinatorial dynamics (types of periodic orbits) (37E15)

Cites Work

• Unnamed Item
• Unnamed Item
• Quadratic maps without asymptotic measure
• Large derivatives, backward contraction and invariant densities for interval maps
• Hyperbolicity, sinks and measure in one dimensional dynamics
• Singular measures without restrictive intervals
• Sur la conjugaison différentiable des difféomorphismes du cercle à des rotations. (On smooth conjugacy of diffeomorphisms of the circle with rotations)
• Absolutely continuous measures for certain maps of an interval
• Absolutely continuous invariant measures for one-parameter families of one-dimensional maps
• 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
• Almost every real quadratic map is either regular or stochastic.
• Exponents, attractors and Hopf decompositions for interval maps
• Positive Liapunov exponents and absolute continuity for maps of the interval
• Real bounds, ergodicity and negative Schwarzian for multimodal maps

This page was built for publication: Critical covering maps without absolutely continuous invariant probability measure