Non existence of attractors and dynamics around some wild homoclinic classes

2010/03/11 by Rafaël Potrie, Rafael Potrie, Potrie, Rafael
Mathematics · Physics and Astronomy · #Advanced Differential Equations and Dynamical Systems #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Dynamics and Fractals #Quantum chaos and dynamical systems #math.DS

paper · pdf · doi:10.48550/arxiv.1003.2280

14 pages. Some remarks added

openalex publication_date 2010/03/11 · arxiv created 2010/05/22 · arxiv updated 2010/05/25 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

We present new examples of generic diffeomorphisms without attractors. Also, we study how these wild classes are accumulated by infinitely many other classes (obtaining that the chain recurrence classes different from the only quasi-attractor are contained in center stable manifolds). The construction relies on some derived from Anosov (DA) constructions and uses strongly the semiconjugacy obtained by these diffeomorphisms. An interesting feature of this examples is that we can show that robustly, they present a unique attractor in the sense of Milnor.

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