Metric properties of non-renormalizableS-unimodal maps. Part I: Induced expansion and invariant measures

DOI10.1017/S0143385700008130zbMath0830.58019OpenAlexW2004978972MaRDI QIDQ4316574

Michael Jakobson, Grzegorz Świątek

Publication date: 28 January 1996

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

Full work available at URL: https://doi.org/10.1017/s0143385700008130

zbMATH Keywords

invariant measuremetric propertiesexpanding mapsMilnor's conjecturenon-renormalizable \(S\)-unimodal maps

Mathematics Subject Classification ID

Ergodic theory (37A99) Dynamical systems with hyperbolic behavior (37D99)

Related Items (9)

Induced maps, Markov extensions and invariant measures in one-dimensional dynamics ⋮ Yet another induction scheme for non-uniformly expanding transformations ⋮ The dynamics of complex box mappings ⋮ On Hausdorff dimension of unimodal attractors ⋮ Invariant measures exist without a growth condition ⋮ Hausdorff dimension of Julia sets in the logistic family ⋮ Topological conditions for the existence of absorbing Cantor sets ⋮ A starting condition approach to parameter distortion in generalized renormalization ⋮ Decay of geometry for Fibonacci critical covering maps of the circle

Cites Work

• Quadratic maps without asymptotic measure
• Distortion of S-unimodal maps
• On the concept of attractor
• Singular measures without restrictive intervals
• Absolutely continuous measures for certain maps of an interval
• Absolutely continuous invariant measures for one-parameter families of one-dimensional maps
• The iteration of cubic polynomials. II: Patterns and parapatterns
• Invariant measures exist under a summability condition for unimodal maps
• The Fibonacci Unimodal Map

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