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Conditional variational principle for the irregular set in some nonuniformly hyperbolic systems

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  • This article is devoted to the study of the irregular sets of Birkhoff averages in some nonuniformly hyperbolic systems via Pesin theory. Particularly, we give a conditional variational principle for the topological entropy of the irregular sets. Our result can be applied (i) to the diffeomorphisms on surfaces, (ii) to the nonuniformly hyperbolic diffeomorphisms described by Katok.
    Mathematics Subject Classification: Primary: 37B40, 37C45; Secondary: 37D25.


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