Conditional variational principle for the irregular set in some nonuniformly hyperbolic systems
Zheng Yin Ercai Chen
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.
keywords: Pesin set Irregular set topological entropy.

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