54 citations · 123 across the 13 of their papers we have counts for
16 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 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…
Smooth representations of unit groups of split basic algebras over non-Archimedean local fields
Carlos A. M. André, João Dias
We consider smooth representations of the unit group of a finite-dimensional split basic algebra over a non-Archimedean local field. In par…
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…