Journal article
Martin Andersson, Pablo D. Carrasco, Radu Saghin
arXiv:2206.08295
arXiv:2206.08295
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APA
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Andersson, M., Carrasco, P. D., & Saghin, R. Non-uniformly hyperbolic endomorphisms. ArXiv:2206.08295.
Chicago/Turabian
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Andersson, Martin, Pablo D. Carrasco, and Radu Saghin. “Non-Uniformly Hyperbolic Endomorphisms.” arXiv:2206.08295 (n.d.).
MLA
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Andersson, Martin, et al. “Non-Uniformly Hyperbolic Endomorphisms.” ArXiv:2206.08295.
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@article{martin-a,
title = {Non-uniformly hyperbolic endomorphisms},
journal = {arXiv:2206.08295},
author = {Andersson, Martin and Carrasco, Pablo D. and Saghin, Radu}
}
We show that in nearly every homotopy class of any non-invertible endomorphism of the two-torus there exists a C^1 open set of non-uniformly hyperbolic area preserving maps (one positive and one negative exponent at Lebesgue almost every point), without dominated splitting. Moreover, these maps are continuity points of the (averaged) Lyapunov exponents and, under a mild assumption on their linear part, they are also stably ergodic: any C^2 conservative C^1 nearby map is ergodic, and in fact metrically isomorphic to a Bernoulli shift.
