An Elementary Proof for Hyperbolicity and Chaos of the Logistic Maps

DOI10.1080/10236190410001652810zbMath1062.37024OpenAlexW2067568020MaRDI QIDQ4658736

Aulbach, Bernd, Bernd Kieninger

Publication date: 18 March 2005

Published in: Journal of Difference Equations and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/10236190410001652810

zbMATH Keywords

chaoslogistic maphyperbolicitymaximal invariant set

Mathematics Subject Classification ID

Strange attractors, chaotic dynamics of systems with hyperbolic behavior (37D45) Dynamical systems with hyperbolic orbits and sets (37D05) Dynamical systems involving maps of the interval (37E05)

Related Items (8)

Anti-integrability for the logistic maps ⋮ Hyperbolicity of the invariant sets for the real polynomial maps ⋮ Denseness of radial-basis functions in \(L^ 2(R^ n)\) and its applications in neural networks ⋮ Period 3 and chaos for unimodal maps ⋮ On the chaotic behavior of a generalized logistic \(p\)-adic dynamical system ⋮ On expanding maps and topological conjugacy ⋮ Bernd Aulbach—Obituary ⋮ Li–Yorke chaos in higher dimensions: a review

Cites Work

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• Sensitive dependence to initial conditions for one dimensional maps
• The abundance of wild hyperbolic sets and non-smooth stable sets for diffeomorphisms
• Absolutely continuous measures for certain maps of an interval
• Hyperbolicity of the invariant set for the logistic map with \(\mu>4\).
• Chaos, Cantor Sets, and Hyperbolicity for the Logistic Maps
• Almost Sure Escape from the Unit Interval under the Logistic Map
• Complex analytic dynamics on the Riemann sphere

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