54 citations · 123 across the 13 of their papers we have counts for
14 papers · 1 filter
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 provid…
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…
Billiards in generic convex bodies have positive topological entropy
Mário Bessa, Gianluigi Del Magno, João Lopes Dias +2
We show that there exists a open dense set of convex bodies with smooth boundary whose billiard map exhibits a non-trivial hyperbolic basic set. As a consequence billiards in…
On the attractor of piecewise expanding maps of the interval
Gianluigi Del Magno, João Lopes Dias, Pedro Duarte +1
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 ergo…
Renormalization of Gevrey vector fields with a Brjuno type arithmetical condition
João Lopes Dias, José Pedro Gaivão
We show that in the Gevrey topology, a -torus flow close enough to linear with a unique rotation vector is linearizable as long as satisfies a Brjuno type diophantine co…
On shadowing and hyperbolicity for geodesic flows on surfaces
Mario Bessa, Maria Joana Torres, Joao Lopes Dias
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 considerin…