Journal article
Martin Andersson, Pablo D. Carrasco, Radu Saghin
to appear in Compositio Mathematica
to appear in Compositio Mathematica
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APA
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Andersson, M., Carrasco, P. D., & Saghin, R. Non-uniformly hyperbolic endomorphisms. To Appear in Compositio Mathematica.
Chicago/Turabian
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Andersson, Martin, Pablo D. Carrasco, and Radu Saghin. “Non-Uniformly Hyperbolic Endomorphisms.” to appear in Compositio Mathematica (n.d.).
MLA
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Andersson, Martin, et al. “Non-Uniformly Hyperbolic Endomorphisms.” To Appear in Compositio Mathematica.
BibTeX Click to copy
@article{martin-a,
title = {Non-uniformly hyperbolic endomorphisms},
journal = {to appear in Compositio Mathematica},
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.
