Zobrazeno 1 - 10
of 52
pro vyhledávání: '"Del Magno, Gianluigi"'
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
Autor:
Bessa, Mário, Del Magno, Gianluigi, Lopes Dias, João, Gaivão, José Pedro, Torres, Maria Joana
Publikováno v:
In Advances in Mathematics April 2024 442
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
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
We study dissipative polygonal outer billiards, i.e. outer billiards about convex polygons with a contractive reflection law. We prove that dissipative outer billiards about any triangle and the square are asymptotically periodic, i.e. they have fini
Externí odkaz:
http://arxiv.org/abs/1310.4724
We prove that polygonal billiards with contracting reflection laws exhibit hyperbolic attractors with countably many ergodic SRB measures. These measures are robust under small perturbations of the reflection law, and the tables for which they exist
Externí odkaz:
http://arxiv.org/abs/1302.1462
The purpose of this paper is to study the dynamics of a square billiard with a non-standard reflection law such that the angle of reflection of the particle is a linear contraction of the angle of incidence. We present numerical and analytical argume
Externí odkaz:
http://arxiv.org/abs/1112.1753
In this paper, we prove a criterion for the local ergodicity of non-uniformly hyperbolic symplectic maps with singularities. Our result is an extension of a theorem of Liverani and Wojtkowski.
Comment: 35 pages
Comment: 35 pages
Externí odkaz:
http://arxiv.org/abs/1010.1229