5 papers
Brjuno condition through best approximations and the linearization problem
Nicolas Chevallier, João Lopes Dias, José Pedro Gaivão +2
We consider the classical analytic linearization problem for vector fields on the torus close to a constant vector field . Our goals are twofold. First, we provi…
Generic properties of planar symplectic billiards
Luca Baracco, Olga Bernardi, José Pedro Gaivão
We study generic properties of planar symplectic billiards, a symplectic analogue of classical Birkhoff billiards introduced by P. Albers and S. Tabachnikov. We prove that, for a r…
Multidimensional contracted rotations
Jose Pedro Gaivao, Benito Pires
We study the dynamics of multidimensional contracted rotations and address a problem posed by Y. Bugeaud and J-P. Conze in \textit{Acta Arithmetica} in 1999. More precisely, we sho…
Lyapunov exponents and rigidity in random billiards and standard maps
Gianluigi Del Magno, João Lopes Dias, José Pedro Gaivão
We study random dynamical systems generated by measure-preserving maps, possibly with singularities. For this class of systems, we establish an invariance principle: if all Lyapuno…
Multi-dimensional piecewise contractions are asymptotically periodic
Jose Pedro Gaivao, Benito Pires
Piecewise contractions (PCs) are piecewise smooth maps that decrease distance between pairs of points in the same domain of continuity. The dynamics of a variety of systems is desc…