English

Invariant measures for interval maps with critical points and singularities

Dynamical Systems 2010-08-26 v3

Abstract

We prove that, under a mild summability condition on the growth of the derivative on critical orbits any piecewise monotone interval map possibly containing discontinuities and singularities with infinite derivative (cusp map) admits an ergodic invariant probability measures which is absolutely continuous with respect to Lebesgue measure.

Keywords

Cite

@article{arxiv.0805.2099,
  title  = {Invariant measures for interval maps with critical points and singularities},
  author = {Vitor Araujo and Stefano Luzzatto and Marcelo Viana},
  journal= {arXiv preprint arXiv:0805.2099},
  year   = {2010}
}

Comments

15 pages, 1 Figure

R2 v1 2026-06-21T10:40:31.290Z