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… 

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