Wild Milnor attractors accumulated by lower-dimensional dynamics
Copyright policy )Wild Milnor attractors accumulated by lower-dimensional dynamics
AbstractWe present new examples of open sets of diffeomorphisms such that generic diffeomorphisms in those sets have no dynamically indecomposable attractors in the topological sense and have infinitely many chain-recurrence classes. We show that all other classes except one are contained in periodic surfaces. This study allows us to obtain the existence of Milnor attractors as well as study ergodic properties of the diffeomorphisms in those open sets by using ideas and results from Bonatti and Viana [SRB measures for partially hyperbolic diffeomorphisms whose central direction is mostly contracting. Israel J. Math.115 (2000), 157–193] and Buzzi and Fisher [Entropic stability beyond partial hyperbolicity. Preprint, 2011, arXiv:1103:2707].
- Paris 13 University France
- University of the Republic Uruguay
Algebraic ergodic theory, cocycles, orbit equivalence, ergodic equivalence relations, recurrence, indecomposable attractor, Stability of topological dynamical systems, Ergodicity, mixing, rates of mixing, Dynamical Systems (math.DS), FOS: Mathematics, Notions of recurrence and recurrent behavior in topological dynamical systems, Milnor attractor, Mathematics - Dynamical Systems, Smooth ergodic theory, invariant measures for smooth dynamical systems
Algebraic ergodic theory, cocycles, orbit equivalence, ergodic equivalence relations, recurrence, indecomposable attractor, Stability of topological dynamical systems, Ergodicity, mixing, rates of mixing, Dynamical Systems (math.DS), FOS: Mathematics, Notions of recurrence and recurrent behavior in topological dynamical systems, Milnor attractor, Mathematics - Dynamical Systems, Smooth ergodic theory, invariant measures for smooth dynamical systems
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