Topological conditions for the existence of invariant measures for unimodal maps

DOI10.1017/S0143385700007963zbMath0812.58052WikidataQ59184917 ScholiaQ59184917MaRDI QIDQ4314695

Henk Bruin

Publication date: 16 May 1995

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

zbMATH Keywords

absolutely continuous measureunimodal maps

Mathematics Subject Classification ID

Measure-preserving transformations (28D05) Entropy in general topology (54C70) Ergodic theory (37A99)

Related Items (12)

Induced maps, Markov extensions and invariant measures in one-dimensional dynamics ⋮ The Lyapunov exponent of holomorphic maps ⋮ Invariant measures exist without a growth condition ⋮ Non-monotonicity of entropy of interval maps ⋮ Large derivatives, backward contraction and invariant densities for interval maps ⋮ Quadratic dynamics in binary number systems ⋮ Wild attractors and thermodynamic formalism ⋮ Topological conditions for the existence of absorbing Cantor sets ⋮ A partial classification of inverse limit spaces of tent maps with periodic critical points ⋮ On the Lebesgue measure of Li-Yorke pairs for interval maps ⋮ Topological properties of Lorenz maps derived from unimodal maps ⋮ Accessible points of planar embeddings of tent inverse limit spaces

Cites Work

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• Quadratic maps without asymptotic measure
• Singular measures without restrictive intervals
• Sensitive dependence to initial conditions for one dimensional maps
• Topological entropy of the transformation \(x\mapsto ax(1-x)\)
• Sur la conjugaison différentiable des difféomorphismes du cercle à des rotations. (On smooth conjugacy of diffeomorphisms of the circle with rotations)
• Julia-Fatou-Sullivan theory for real one-dimensional dynamics
• A structure theorem in one dimensional dynamics
• Invariant measures exist under a summability condition for unimodal maps
• Markov partition in non-hyperbolic interval dynamics
• Representations for real numbers and their ergodic properties
• The Fibonacci Unimodal Map

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