35 citations · 60 across the 15 of their papers we have counts for
23 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…
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…
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…
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…
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…
Rotation number of 2-interval piecewise affine maps
José Pedro Gaivao, Michel Laurent, Arnaldo Nogueira
We study maps of the unit interval whose graph is made up of two increasing segments and which are injective in an extended sense. Such maps $f_{\p}$ are parametrized by a quintupl…
Hausdorff dimension of the exceptional set of interval piecewise affine contractions
José Pedro Gaivão
Let , and be a piecewise -affine map of the interval , i.e., there exist a partition of the interval …
Chaotic time series in financial processes consisting of savings with piecewise constant monthly contributions
José Pedro Gaivão, Benito Pires
We investigate the time series generated by an elementary and deterministic financial process that consists in making monthly contributions to a savings account subjected to the de…
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…
Dynamics of piecewise increasing contractions
José Pedro Gaivão, Arnaldo Nogueira
Let be a partition of the interval into subintervals. Let be a map such that each restriction is an…
Periodic attractor in the discrete time best-response dynamics of the Rock-Paper-Scissors game
José Pedro Gaivão, Telmo Peixe
The Rock-Paper-Scissors (RPS) game is a classic non-cooperative game widely studied in terms of its theoretical analysis as well as in its applications, ranging from sociology and…
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…
Asymptotic periodicity in outer billiards with contraction
José Pedro Gaivão
We show that for almost every where is a convex polygon and , the corresponding outer billiard about with contraction is asymptotically periodic, i.e…
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…
-stability of periodic billiard orbits
José Pedro Gaivão, Serge Troubetzkoy
We introduce a new notion of stability for periodic orbits in polygonal billiards. We say that a periodic orbit of a polygonal billiard is -stable if there is a periodic orbit f…
Hyperbolic billiards on polytopes with contracting reflection laws
Pedro Duarte, José Pedro Gaivão, Mohammad Soufi
We study billiards on polytopes in $\Rr^d$ with contracting reflection laws, i.e. non-standard reflection laws that contract the reflection angle towards the normal. We prove that…
Hyperbolic polygonal billiards with finitely many ergodic SRB measures
Gianluigi Del Magno, João Lopes Dias, Pedro Duarte +1
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,…
Hyperbolic polygonal billiards close to 1-dimensional piecewise expanding maps
Gianluigi Del Magno, João Lopes Dias, Pedro Duarte +1
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 ha…
Dissipative outer billiards: a case study
Gianluigi Del Magno, José Pedro Gaivão, Eugene Gutkin
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 tr…
SRB measures for hyperbolic polygonal billiards
Gianluigi Del Magno, João Lopes Dias, Pedro Duarte +2
We prove that polygonal billiards with contracting reflection laws exhibit hyperbolic attractors with countably many ergodic SRB measures. These measures are robust under small per…
Chaos in the square billiard with a modified reflection law
Gianluigi Del Magno, João Lopes Dias, Pedro Duarte +2
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…
Analytic invariants for the resonance
Jose Pedro Gaivao
Associated to analytic Hamiltonian vector fields in having an equilibrium point satisfying a non semisimple resonance, we construct two universal constants th…
Splitting of separatrices for the Hamiltonian-Hopf bifurcation with the Swift-Hohenberg equation as an example
Jose Pedro Gaivao, Vassili Gelfreich
We study homoclinic orbits of the Swift-Hohenberg equation near a Hamiltonian-Hopf bifurcation. It is well known that in this case the normal form of the equation is integrable at…