# Non-uniformly hyperbolic endomorphisms

### Journal article

Martin Andersson, Pablo D. Carrasco, Radu Saghin
arXiv:2206.08295

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### Cite

APA
Andersson, M., Carrasco, P. D., & Saghin, R. Non-uniformly hyperbolic endomorphisms. ArXiv:2206.08295.

Chicago/Turabian
Andersson, Martin, Pablo D. Carrasco, and Radu Saghin. “Non-Uniformly Hyperbolic Endomorphisms.” arXiv:2206.08295 (n.d.).

MLA
Andersson, Martin, et al. “Non-Uniformly Hyperbolic Endomorphisms.” ArXiv:2206.08295.

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.

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