The abundance of strange attractor in the families of nearby singular diffeomorphism

DOI10.1007/BF02560528zbMath0889.58052OpenAlexW49668998MaRDI QIDQ4358835

Yong-Luo Cao

Publication date: 8 June 1998

Published in: Acta Mathematica Sinica (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf02560528

zbMATH Keywords

strange attractorMisiurewicz conditiontransversal homoclinic pointunimodal mappingHenon-like strange attractornearby singular diffeomorphism

Mathematics Subject Classification ID

Attractors and repellers of smooth dynamical systems and their topological structure (37C70) Strange attractors, chaotic dynamics of systems with hyperbolic behavior (37D45)

Cites Work

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• The dynamics of the Hénon map
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• Hyperbolicity, sinks and measure in one dimensional dynamics
• On iterations of \(1-\alpha x^2\) on \((-1,1)\)
• On the abundance of aperiodic behaviour for maps on the interval
• Absolutely continuous invariant measures for one-parameter families of one-dimensional maps
• Positive Lyapunov exponents in families of one dimensional dynamical systems
• Abundance of strange attractors
• Sinai-Bowen-Ruelle measures for certain Hénon maps
• Continuous measures in one dimension
• Another proof of Jakobson's Theorem and related results
• Measurable dynamics of $S$-unimodal maps of the interval

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