Thick attractors of step skew products

被引:0
作者
Yu. Ilyashenko
机构
[1] Cornell University,V.A. Steklov Mathematical Institute
[2] RAS,undefined
来源
Regular and Chaotic Dynamics | 2010年 / 15卷
关键词
attractor; diffeomorphism; step skew product; 37Cxx;
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摘要
A diffeomorphism is said to have a thick attractor provided that its Milnor attractor has positive but not full Lebesgue measure. We prove that there exists an open set in the space of boundary preserving step skew products with a fiber [0,1], such that any map in this set has a thick attractor.
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页码:328 / 334
页数:6
相关论文
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[1]  
Kan I.(1994)Open Sets of Difeomorphisms Having Two Attractors, Each with Everywhere Dense Basin Bull. Amer. Math. Soc. 31 68-74
[2]  
Gorodetskii A. S.(1999)Some New Robust Properties of Invariant Sets and Attractors of Dynamical Systems Funktsional. Anal. i Prilozhen. 33 16-30
[3]  
Ilyashenko Yu. S.(2008)Diffeomorphisms with Intermingled Attracting Basins Funkts. Anal. i Prilozh. 42 60-71
[4]  
Ilyashenko Yu.(2008)Openness of the Set of Boundary Preserving Maps of an Annulus with Intermingled Attracting Basins J. Fixed Point Theory Appl. 3 449-463
[5]  
Ilyashenko Yu.(1978)Topology of Phase Portraits of Analytic Differential Equations in the Complex Projective Plane Tr. Semin. im. I. G. Petrovskogo 4 83-136
[6]  
Kleptsyn V.(1991)The Concept of Minimal Attractors and Maximal Attractors of Partial Differential Equations of the Kuramoto-Sivashinski Type Chaos 1 168-173
[7]  
Saltykov P.(1996)Minimal and Strange Attractors: Nonlinear Dynamics, Bifurcations and Chaotic Behavior Internat. J. Bifur. Chaos Appl. Sci. Engrg. 6 1177-1183
[8]  
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