Topological and metrical conditions for Collet-Eckmann unimodal maps

DOI10.1007/BF02677379zbMath1154.37342MaRDI QIDQ5949527

Lan Yu Wang

Publication date: 21 November 2001

Published in: Acta Mathematicae Applicatae Sinica. English Series (Search for Journal in Brave)

zbMATH Keywords

Schwarzian derivativekneading invariantCollet-Eckmann mapunimodal map

Mathematics Subject Classification ID

Topological dynamics (37B99) Dynamical systems involving maps of the interval (37E05)

Cites Work

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• The dynamics of the Hénon map
• Quadratic maps without asymptotic measure
• On iterations of \(1-\alpha x^2\) on \((-1,1)\)
• Sensitive dependence to initial conditions for one dimensional maps
• Topological entropy of the transformation \(x\mapsto ax(1-x)\)
• Absolutely continuous invariant measures for one-parameter families of one-dimensional maps
• Spectral theory, zeta functions and the distribution of periodic points for Collet-Eckmann maps
• Positive Lyapunov exponents in families of one dimensional dynamical systems
• Positive Lyapunov exponent for generic one-parameter families of unimodal maps
• Positive Liapunov exponents and absolute continuity for maps of the interval
• A positive Liapunov exponent for the critical value of an S-unimodal mapping implies uniform hyperbolicity
• On the abundance of chaotic behavior for generic one-parameter families of maps
• Symmetric S-unimodal mappings and positive Liapunov exponents

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