Arturo Vieiro
Gran Via 585, 08007, Barcelona, Catalunya
Departament de Matematica Aplicada i Analisi, Universitat de Barcelona
Publications:
Miguel N., Simó C., Vieiro A.
Escape Times Across the Golden Cantorus of the Standard Map
2022, vol. 27, no. 3, pp. 281306
Abstract
We consider the Chirikov standard map for values of the parameter
larger than but close to Greene's $k_G$. We investigate the dynamics near the
golden Cantorus and study escape rates across it.
Mackay [17, 19]
described the behaviour of the mean of the number of iterates
$\langle N_k \rangle$ to cross the Cantorus as $k\to k_G$ and showed that there
exists $B<0$ so that $\langle N_k\rangle (kk_G)^B$ becomes 1periodic in a
suitable logarithmic scale. The numerical explorations here give evidence of
the shape of this periodic function and of the relation between the escape
rates and the evolution of the stability islands close to the Cantorus.

Fontich E., Simó C., Vieiro A.
On the “Hidden” Harmonics Associated to Best Approximants Due to Quasiperiodicity in Splitting Phenomena
2018, vol. 23, no. 6, pp. 638653
Abstract
The effects of quasiperiodicity on the splitting of invariant manifolds are examined. We have found that some harmonics that could be expected to be dominant in some ranges of the perturbation parameter actually are nondominant. It is proved that, under reasonable conditions, this is due to the arithmetic properties of the frequencies.

Miguel N., Simó C., Vieiro A.
From the Hénon Conservative Map to the Chirikov Standard Map for Large Parameter Values
2013, vol. 18, no. 5, pp. 469489
Abstract
In this paper we consider conservative quadratic Hénon maps and Chirikov’s standard map, and relate them in some sense.
First, we present a study of some dynamical properties of orientationpreserving and orientationreversing quadratic Hénon maps concerning the stability region, the size of the chaotic zones, its evolution with respect to parameters and the splitting of the separatrices of fixed and periodic points plus its role in the preceding aspects. Then the phase space of the standard map, for large values of the parameter k, is studied. There are some stable orbits which appear periodically in $k$ and are scaled somehow. Using this scaling, we show that the dynamics around these stable orbits is one of the above Hénon maps plus some small error, which tends to vanish as $k \to \infty$. Elementary considerations about diffusion properties of the standard map are also presented. 