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Anosov diffeomorphism with a horseshoe that attracts almost any point

Autor: Bonatti, C., Minkov, S., Okunev, A., Shilin, I.

We present an example of a C1 Anosov diffeomorphism of a two-torus with a physical measure such that its basin has full Lebesgue measure and its support is a horseshoe of zero measure.
Comment: 19 pages, 3 figures. Rewrote the second page of Int

Externí odkaz: http://arxiv.org/abs/1802.03977

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Akademický článek

On a quadratic form associated with a surface automorphism and its applications to Singularity Theory

Autor: Alanís-López, L., Artal, E., Bonatti, C., Gómez-Mont, X., González Villa, M., Portilla Cuadrado, P.

Publikováno v: In Indagationes Mathematicae July 2022 33(4):816-843

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Rigidity for $C^1$ actions on the interval arising from hyperbolicity I: solvable groups

Autor: Bonatti, C., Monteverde, I., Navas, A., Rivas, C.

We consider Abelian-by-cyclic groups for which the cyclic factor acts by hyperbolic automorphisms on the Abelian subgroup. We show that if such a group acts faithfully by $C^1$ diffeomorphisms of the closed interval with no global fixed point at the

Externí odkaz: http://arxiv.org/abs/1309.5277

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Abundance of $C^1$-robust homoclinic tangencies

Autor: Bonatti, C., Diaz, L. J.

A diffeomorphism $f$ has a $C^1$-robust homoclinic tangency if there is a $C^1$-neighbourhood $\cU$ of $f$ such that every diffeomorphism in $g\in \cU$ has a hyperbolic set $\La_g$, depending continuously on $g$, such that the stable and unstable man

Externí odkaz: http://arxiv.org/abs/0909.4062

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A C^1 -Generic dichotomy for diffeomorphisms

Autor: Bonatti, C., Diaz, L. J., Pujals, E. R.

Publikováno v: Ann. of Math. (2), vol. 158 (2003), no.2, 355--418

We show that, for every compact n-dimensional manifold, n\geq 1, there is a residual subset of Diff^1(M) of diffeomorphisms for which the homoclinic class of any periodic saddle of f verifies one of the following two possibilities: Either it is conta

Externí odkaz: http://arxiv.org/abs/math/0610527

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