# Genericity of historic behavior for maps and flows

@article{Carvalho2021GenericityOH, title={Genericity of historic behavior for maps and flows}, author={Maria Carvalho and Paulo Varandas}, journal={Nonlinearity}, year={2021}, volume={34}, pages={7030 - 7044} }

We establish a sufficient condition for a continuous map, acting on a compact metric space, to have a Baire residual set of points exhibiting historic behavior (also known as irregular points). This criterion applies, for instance, to a minimal and non-uniquely ergodic map; to maps preserving two distinct probability measures with full support; to non-trivial homoclinic classes; to some non-uniformly expanding maps; and to partially hyperbolic diffeomorphisms with two periodic points whose…

## 9 Citations

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### HISTORIC BEHAVIOR FOR FLOWS WITH THE GLUING ORBIT PROPERTY

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We consider the set of points with historic behavior (which is also called the irregular set) for continuous flows and suspension flows. In this paper under the hypothesis that (Xt)t is a continuous…

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