pdcarrasco - Non-uniformly hyperbolic endomorphisms

Journal article

Martin Andersson, Pablo D. Carrasco, Radu Saghin
Compositio Mathematica, vol. 161(6), 2025, pp. 1313 - 1356

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APA Click to copy
Andersson, M., Carrasco, P. D., & Saghin, R. (2025). Non-uniformly hyperbolic endomorphisms. Compositio Mathematica, 161(6), 1313–1356. https://doi.org/10.1112/S0010437X2500702X

Chicago/Turabian Click to copy
Andersson, Martin, Pablo D. Carrasco, and Radu Saghin. “Non-Uniformly Hyperbolic Endomorphisms.” Compositio Mathematica 161, no. 6 (2025): 1313–1356.

MLA Click to copy
Andersson, Martin, et al. “Non-Uniformly Hyperbolic Endomorphisms.” Compositio Mathematica, vol. 161, no. 6, 2025, pp. 1313–56, doi:10.1112/S0010437X2500702X.

BibTeX Click to copy

@article{martin2025a,
  title = {Non-uniformly hyperbolic endomorphisms},
  year = {2025},
  issue = {6},
  journal = {Compositio Mathematica},
  pages = {1313 - 1356},
  volume = {161},
  doi = {10.1112/S0010437X2500702X},
  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.