Typical points and families of expanding interval mappings

Tomas Persson

Typical points and families of expanding interval mappings

Dynamical Systems 2015-06-19 v2

Authors: Tomas Persson

Abstract

We study parametrised families of piecewise expanding interval mappings $T_a \colon [0,1] \to [0,1]$ with absolutely continuous invariant measures $\mu_a$ and give sufficient conditions for a point $X(a)$ to be typical with respect to $(T_a, \mu_a)$ for almost all parameters $a$ . This is similar to a result by D. Schnellmann, but with different assumptions.

Keywords

typical points expanding interval mappings parametrised families absolutely continuous invariant measures piecewise expanding maps dynamical systems

Cite

@article{arxiv.1505.07211,
  title  = {Typical points and families of expanding interval mappings},
  author = {Tomas Persson},
  journal= {arXiv preprint arXiv:1505.07211},
  year   = {2015}
}

Comments

16 pages, 2 figures. Minor corrections made. Some remarks have been added thanks to comments by D. Schnellmann

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