Inverse SRB measures for endomorphisms on surfaces

Fuente: arXiv
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Autori principali: Janeiro, Victor, Saghin, Radu
Natura: Preprint
Pubblicazione: 2025
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author Janeiro, Victor
Saghin, Radu
author_facet Janeiro, Victor
Saghin, Radu
contents We extend D. Burguet's construction of SRB measures for the non invertible scenario obtaining hyperbolic invariant measures with absolutely continuous disintegrations on stable manifolds for a certain class of endomorphisms on the two torus. The constructed measures maximize the folding entropy, in particular, one may obtain such SRB measures for conservative perturbations of the examples given by M. Andersson, P. Carrasco and R. Saghin for which the Lebesgue measure does not maximize the folding entropy. This way, we obtain examples of topologically mixing maps with at least two inverse SRB measures. In the case of inverse SRB measures that maximize the folding entropy, we give criteria for uniqueness.
format Preprint
id arxiv_https___arxiv_org_abs_2512_09624
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Inverse SRB measures for endomorphisms on surfaces
Janeiro, Victor
Saghin, Radu
Dynamical Systems
37C40 (Primary) 37A05, 37D25 (Secondary)
We extend D. Burguet's construction of SRB measures for the non invertible scenario obtaining hyperbolic invariant measures with absolutely continuous disintegrations on stable manifolds for a certain class of endomorphisms on the two torus. The constructed measures maximize the folding entropy, in particular, one may obtain such SRB measures for conservative perturbations of the examples given by M. Andersson, P. Carrasco and R. Saghin for which the Lebesgue measure does not maximize the folding entropy. This way, we obtain examples of topologically mixing maps with at least two inverse SRB measures. In the case of inverse SRB measures that maximize the folding entropy, we give criteria for uniqueness.
title Inverse SRB measures for endomorphisms on surfaces
topic Dynamical Systems
37C40 (Primary) 37A05, 37D25 (Secondary)
url https://arxiv.org/abs/2512.09624