Non-uniformly hyperbolic endomorphisms

Journal article

Martin Andersson, Pablo D. Carrasco, Radu Saghin

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

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

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

BibTeX   Click to copy

  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.


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