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pro vyhledávání: '"Dias, João Lopes"'
Autor:
Bessa, Mário, Del Magno, Gianluigi, Dias, João Lopes, Gaivão, José Pedro, Torres, Maria Joana
We show that there exists a $C^2$ open dense set of convex bodies with smooth boundary whose billiard map exhibits a non-trivial hyperbolic basic set. As a consequence billiards in generic convex bodies have positive topological entropy and exponenti
Externí odkaz:
http://arxiv.org/abs/2201.01362
We consider piecewise expanding maps of the interval with finitely many branches of monotonicity and show that they are generically combinatorially stable, i.e., the number of ergodic attractors and their corresponding mixing periods do not change un
Externí odkaz:
http://arxiv.org/abs/1711.06554
Autor:
Dias, João Lopes, Gaivão, José Pedro
We show that in the Gevrey topology, a $d$-torus flow close enough to linear with a unique rotation vector $\omega$ is linearizable as long as $\omega$ satisfies a Brjuno type diophantine condition. The proof is based on the fast convergence under re
Externí odkaz:
http://arxiv.org/abs/1706.04510
Akademický článek
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Publikováno v:
Nonlinear Analysis: Theory, Methods & Applications, Vol. 155, 250-263 (2017)
We prove that the geodesic flow on closed surfaces displays a hyperbolic set if the shadowing property holds C2-robustly on the metric. Similar results are obtained when considering even feeble properties like the weak shadowing and the specification
Externí odkaz:
http://arxiv.org/abs/1605.03332
We study polygonal billiards with reflection laws contracting the reflected angle towards the normal. It is shown that if a polygon does not have parallel sides facing each other, then the corresponding billiard map has finitely many ergodic SRB meas
Externí odkaz:
http://arxiv.org/abs/1507.06250
We consider polygonal billiards with collisions contracting the reflection angle towards the normal to the boundary of the table. In previous work, we proved that such billiards has a finite number of ergodic SRB measures supported on hyperbolic gene
Externí odkaz:
http://arxiv.org/abs/1501.03697
Polygonal slap maps are piecewise affine expanding maps of the interval obtained by projecting the sides of a polygon along their normals onto the perimeter of the polygon. These maps arise in the study of polygonal billiards with non-specular reflec
Externí odkaz:
http://arxiv.org/abs/1312.1314
Publikováno v:
DCDS-A Volume 34, Issue 12, December 2014
We prove that any perturbation of the symplectic part of the derivative of a Poisson diffeomorphism can be realized as the derivative of a $C^1$-close Poisson diffeomorphism. We also show that a similar property holds for the Poincar\'e map of a Hami
Externí odkaz:
http://arxiv.org/abs/1310.1063