STATISTICAL PROPERTIES OF ONE-DIMENSIONAL MAPS WITH CRITICAL POINTS AND SINGULARITIES

By K. Diaz-Ordaz, Mark Holland, Stefano Luzzatto. 2006

51 citations recorded by the source corpus.

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 Holder observations.

Subfields: Mathematical Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/f75fb864c333632e71ebb9bb4f568b0b2537d597

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In Mathematical Physics

In Statistical and Nonlinear Physics

Citations in the corpus

On the validity of the 0–1 test for chaos (2009, background): “In the case of quasiperiodic dynamics, we require additional smoothness assumptions on the observable v.”
Homoclinic and heteroclinic bifurcations in vector fields (2010, background): “For an analysis of the dynamics of interval maps with both singularities and critical points that yield approximate one-dimensional models for these attractors, see [110, 263, 264].”
SRB measures for partially hyperbolic systems whose central direction is weakly expanding (2014, unknown): “…discussion to dif-feomorphisms, but the same kind of questions, and the Palis conjecture, also apply to endomorphisms—see for example [9, 10, 17, 24, 32, 31] for the setting of one-dimensional maps, [45] in two dimensions, and [5, 6, 40, 41] for the construction of SRB measures in certain…”
The Lorenz Attractor is Mixing (2004, background): “The existence of a Gibbs-Markov induced map is a very general condition, see [7, 3]. It clearly holds for uniformly expanding maps and, we have made use of the recent work [9, 10 ] for Lorenz-like expanding maps.”