Exact upper bounds for the number of one-dimensional basic sets of surface \(A\)-diffeomorphisms

DOI10.1007/BF02471759zbMath0995.37015OpenAlexW2028313536MaRDI QIDQ1972734

A. Yu. Zhirov, R. V. Plykin, Evgeny Zhuzhoma, Samuel Kh. Aranson

Publication date: 13 April 2000

Published in: Journal of Dynamical and Control Systems (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf02471759

zbMATH Keywords

attractorshyperbolic attractororientable surfacenon-orientable surfacerepellers\(A\)-diffeomorphismshyperbolic repellermaximal number of one-dimensional basic setsthorn index

Mathematics Subject Classification ID

Attractors and repellers of smooth dynamical systems and their topological structure (37C70) Uniformly hyperbolic systems (expanding, Anosov, Axiom A, etc.) (37D20)

Related Items (4)

Heteroclinic orbits between rotating waves in hyperbolic balance laws ⋮ On decomposition of ambient surfaces admitting \(A\)-diffeomorphisms with non-trivial attractors and repellers ⋮ Dynamical Systems with Nontrivially Recurrent Invariant Manifolds ⋮ On structurally stable diffeomorphisms with codimension one expanding attractors

Cites Work

• Quadratic differentials with prescribed singularities and pseudo-Anosov diffeomorphisms
• On the relationship between one-dimensional hyperbolic attractors of surface diffeomorphisms and generalized pseudo-Anosov diffeomorphisms
• The topological classification of cascades on closed two-dimensional manifolds
• ON THE STRUCTURE OF QUASIMINIMAL SETS OF FOLIATIONS ON SURFACES
• Differentiable dynamical systems
• THE TOPOLOGY OF BASIS SETS FOR SMALE DIFFEOMORPHISMS

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