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- Arc exchange systems and renormalizationPublication . Pinto, Alberto A.; Rand, David A.; Ferreira, FlávioWe exhibit the construction of stable arc exchange systems from the stable laminations of hyperbolic diffeomorphisms. We prove a one-to-one correspondence between (i) Lipshitz conjugacy classes of C(1+H) stable arc exchange systems that are C(1+H) fixed points of renormalization and (ii) Lipshitz conjugacy classes of C(1+H) diffeomorphisms f with hyperbolic basic sets Lambda that admit an invariant measure absolutely continuous with respect to the Hausdorff measure on Lambda. Let HD(s)(Lambda) and HD(u)(Lambda) be, respectively, the Hausdorff dimension of the stable and unstable leaves intersected with the hyperbolic basic set L. If HD(u)(Lambda) = 1, then the Lipschitz conjugacy is, in fact, a C(1+H) conjugacy in (i) and (ii). We prove that if the stable arc exchange system is a C(1+HDs+alpha) fixed point of renormalization with bounded geometry, then the stable arc exchange system is smooth conjugate to an affine stable arc exchange system.
- Atractor de Lorenz: efeito borboletaPublication . Ferreira, Fernanda A.Este trabalho consiste numa descriçao da importante descoberta obtida por E. Lorenz quando trabalhava num modelo para previsão meteorológica: o efeito borboleta. Na resolução de um sistema por processos iterativos, Lorenz verificou que uma simples diferença na ordem das décimas de milésimas e numa só variavel traduzia-se em soluções completamente diferentes das anteriores obtidas. Este efeito reflecte a sensibilidade às condições iniciais do sistema, que é uma característica essencial dos sistemas caõticos, e observável em áreas da ciência tão diferentes, como a Matemática, a Física, a Biologia, a Economia, a Gestao, entre outras.
- Cantor exchange systems and renormalizationPublication . Pinto, Alberto A.; Rand, David A.; Ferreira, FlávioWe prove a one-to-one correspondence between (i) C1+ conjugacy classes of C1+H Cantor exchange systems that are C1+H fixed points of renormalization and (ii) C1+ conjugacy classes of C1+H diffeomorphisms f with a codimension 1 hyperbolic attractor Lambda that admit an invariant measure absolutely continuous with respect to the Hausdorff measure on Lambda. However, we prove that there is no C1+alpha Cantor exchange system, with bounded geometry, that is a C1+alpha fixed point of renormalization with regularity alpha greater than the Hausdorff dimension of its invariant Cantor set.
- Characterizations of power indices based on null player free winning coalitionsPublication . Álvarez-Mozos, M.; Ferreira, Flávio; Alonso-Meijide, J. M.; Pinto, Alberto A.In this paper, we characterize two power indices introduced in [1] using two different modifications of the monotonicity property first stated by [2]. The sets of properties are easily comparable among them and with previous characterizations of other power indices.
- Contingent claim pricing through a continuous time variational bargaining schemePublication . Azevedo, N.; Pinheiro, D.; Xanthopoulos, S. Z.; Yannacopoulos, A. N.We consider a variational problem modelling the evolution with time of two probability measures representing the subjective beliefs of a couple of agents engaged in a continuous-time bargaining pricing scheme with the goal of finding a unique price for a contingent claim in a continuous-time financial market. This optimization problem is coupled with two finite dimensional portfolio optimization problems, one for each agent involved in the bargaining scheme. Under mild conditions, we prove that the optimization problem under consideration here admits a unique solution, yielding a unique price for the contingent claim.
- Dinâmica simbólica e ferradura de SmalePublication . Ferreira, Fernanda A.Descrevemos a “ferradura de Smale”, um sistema dinâmico bem conhecido que apresenta um conjunto de propriedades muito importantes em Sistemas Dinâmicos. O estudo da dinâmica da “ferradura de Smale” permitenos entender a importância do conceito de dinâmica simbólica.
- Dynamic programming for a Markov-switching jump–diffusionPublication . Azevedo, N.; Pinheiro, D.; Weber, G.-W.We consider an optimal control problem with a deterministic finite horizon and state variable dynamics given by a Markov-switching jump–diffusion stochastic differential equation. Our main results extend the dynamic programming technique to this larger family of stochastic optimal control problems. More specifically, we provide a detailed proof of Bellman’s optimality principle (or dynamic programming principle) and obtain the corresponding Hamilton–Jacobi–Belman equation, which turns out to be a partial integro-differential equation due to the extra terms arising from the Lévy process and the Markov process. As an application of our results, we study a finite horizon consumption– investment problem for a jump–diffusion financial market consisting of one risk-free asset and one risky asset whose coefficients are assumed to depend on the state of a continuous time finite state Markov process. We provide a detailed study of the optimal strategies for this problem, for the economically relevant families of power utilities and logarithmic utilities.
- Environmental taxation: privatization with different public firm’s objective functionsPublication . Ferreira, Fernanda A.; Ferreira, FlávioIn this paper, we study the effects of environmental taxes and privatization in a mixed market, by considering that the public firm aims to maximize the social welfare. The model has two stages. In the first stage, the government sets the environmental tax. Then, the firms engage in a Cournot competition, choosing output and pollution abatement levels. We also compare the results obtained with the ones got when the public firm aims to maximize the sum of consumer surplus and the firm’s profit.
- Equilíbrio de Nash versus Óptimo de Pareto: racionalidade individualista versus racionalidade altruístaPublication . Ferreira, Fernanda A.; Ferreira, Flávio
- Explosion of smoothness from a point to everywhere for conjugacies between diffeomorphisms on surfacesPublication . Ferreira, Flávio; Pinto, Alberto A.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.