Invariant measures exist without a growth condition

DOI10.1007/s00220-003-0928-zzbMath1098.37034OpenAlexW2133247387MaRDI QIDQ1411062

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

Publication date: 15 October 2003

Published in: Communications in Mathematical Physics (Search for Journal in Brave)

Full work available at URL: http://epubs.surrey.ac.uk/1520/1/fulltext.pdf

zbMATH Keywords

absolutely continuous probability measurecritical-point-order dependencenon-flat \(S\)-unimodal interval map

Mathematics Subject Classification ID

Dynamical aspects of measure-preserving transformations (37A05) Dynamical systems involving maps of the interval (37E05)

Related Items (14)

On the combinatorics of Fibonacci-like non-renormalizable maps ⋮ The attractor of Fibonacci-like renormalization operator ⋮ Parapuzzle of the Multibrot set and typical dynamics of unimodal maps ⋮ On non-uniform hyperbolicity assumptions in one-dimensional dynamics ⋮ Decay of correlations for Fibonacci unimodal interval maps ⋮ Large derivatives, backward contraction and invariant densities for interval maps ⋮ Characterization of Dynamics of a Class of Polynomial Automorphisms in ℂn ⋮ On cusps and flat tops ⋮ Critical covering maps without absolutely continuous invariant probability measure ⋮ On stochastic stability of expanding circle maps with neutral fixed points ⋮ Non-uniform hyperbolicity in complex dynamics ⋮ Existence of unique SRB-measures is typical for real unicritical polynomial families ⋮ STATISTICAL PROPERTIES OF ONE-DIMENSIONAL MAPS WITH CRITICAL POINTS AND SINGULARITIES ⋮ Invariant measures for interval maps with different one-sided critical orders

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