Statistical properties of one-dimensional maps with critical points and singularities

Details Statistical properties of one-dimensional maps with critical points and singularities Statistical properties of one-dimensional maps with critical points and singularities

2007-09-11

arxiv.org/abs/0709.1723v1

Stochastics and Dynamics, vol 6, issue 4 (2006), pp. 423-458

Mathematics

Dynamical Systems

31 pages

Scientific paper

We prove that a class of one-dimensional maps with an arbitrary number of
non-degenerate critical and singular points admits an induced Markov tower with
exponential return time asymptotics. In particular the map has an absolutely
continuous invariant probability measure with exponential decay of correlations
for H\"{o}lder observations.

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