Exceptional Sets for Nonuniformly Hyperbolic Diffeomorphisms

  • Sara Campos
  • Katrin GelfertEmail author


For a surface diffeomorphism, a compact invariant locally maximal set W and some subset \(A\subset W\) we study the A-exceptional set, that is, the set of points whose orbits do not accumulate at A. We show that if the Hausdorff dimension of A is smaller than the Hausdorff dimension d of some ergodic hyperbolic measure, then the topological entropy of the exceptional set is at least the entropy of this measure and its Hausdorff dimension is at least d. Particular consequences occur when there is some a priori defined hyperbolic structure on W and, for example, if there exists an SRB measure.


Topological entropy Hausdorff dimension Exceptional sets 

Mathematics Subject Classification

37B40 37C45 37D25 37F35 


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Authors and Affiliations

  1. 1.Department of Mathematics, Federal University of Juiz de ForaCampus Universitário - Bairro MartelosJuiz de ForaBrazil
  2. 2.Institute of MathematicsFederal University of Rio de JaneiroRio de JaneiroBrazil

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