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Publications

Publications by Alberto Pinto

2009

CYCLES AND UNIVERSALITY IN SUNSPOT NUMBER FLUCTUATIONS

Authors
Goncalves, R; Pinto, AA; Stollenwerk, N;

Publication
ASTROPHYSICAL JOURNAL

Abstract
We analyze the famous Wolf's sunspot numbers. Surprisingly, we discovered that the distribution of the sunspot number fluctuations for both the ascending and descending phases is close to the universal nonparametric Bramwell-Holdsworth-Pinton (BHP) distribution. Since the BHP probability density function appears in several other physical phenomena, our result reveals a universal feature of the Wolf's sunspot numbers.

2003

Explosion of smoothness from a point to everywhere for conjugacies between diffeomorphisms on surfaces

Authors
Ferreira, F; Pinto, AA;

Publication
ERGODIC THEORY AND DYNAMICAL SYSTEMS

Abstract
For diffeomorphisms on surfaces with basic sets, we show the following type of rigidity result: if a topological conjugacy between them is differentiable at a point in the basic set then the conjugacy has a smooth extension to the surface. These results generalize the similar ones of D. Sullivan, E. de Faria and ours for one-dimensional expanding dynamics.

1995

Classifying C1+ structures on dynamical fractals: 2. Embedded trees

Authors
Pinto, AA; Rand, DA;

Publication
Ergodic Theory and Dynamical Systems

Abstract
We classify the C1+a structures on embedded trees. This extends the results of Sullivan on embeddings of the binary tree to trees with arbitrary topology and to embeddings without bounded geometry and with contact points. We used these results in an earlier paper to describe the moduli spaces of smooth conjugacy classes of expanding maps and Markov maps on train tracks. In later papers we will use those results to do the same for pseudo-Anosov diffeomorphisms of surfaces. These results are also used in the classification of renormalisation limits of C1+a diffeomorphisms of the circle.

2006

Stackelberg duopoly with demand uncertainty

Authors
Pinto, AA; Ferreira, FA; Ferreira, F;

Publication
2006 IEEE International Conference on Computational Cybernetics, ICCC

Abstract
We consider a symmetric Stackelberg model in which there is asymmetric demand information owned by first and second movers. We analyse the advantages of leadership and flexibility, and prove that when the leading firm faces demand uncertainty, but the follower does not, the first mover does not necessarily have advantage over the second mover. Moreover, we show that the advantage of one firm over the other depends upon the demand fluctuation and also upon the degree of substitutability of the products.

2006

Separating sequential equilibrium in a Bayesian international duopoly

Authors
Pinto, AA; Ferreira, FA; Ferreira, F;

Publication
2006 IEEE International Conference on Computational Cybernetics, ICCC

Abstract
We consider two Cournot firms, one located in the home country and the other in the foreign country, producing substitute goods for consumption in a third country. We suppose that neither the home government nor the foreign firm know the costs of the home firm, while the foreign firm cost is common knowledge. We determine the separating sequential equilibrium outputs.

2012

GOLDEN TILINGS

Authors
Pinto, AA; Almeida, JP; Portela, A;

Publication
TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY

Abstract
We introduce the notion of golden tilings, and we prove a one-to-one correspondence between (i) smooth conjugacy classes of Anosov diffeomorphisms, with an invariant measure absolutely continuous with respect to the Lebesgue measure, (ii) affine classes of golden tilings and (iii) solenoid functions. The solenoid functions give a parametrization of the infinite dimensional space consisting of the mathematical objects described in the above equivalences.

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