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- 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.
- 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.
- 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
- 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.
- 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.
- Two new power indices based on winning coalitionsPublication . Alonso-Meijide, J. M.; Ferreira, Flávio; Álvarez-Mozos, M.; Pinto, Alberto A.Deegan and Packel (1979) and Holler (1982) proposed two power indices for simple games: the Deegan–Packel index and the Public Good Index. In the definition of these indices, only minimal winning coalitions are taken into account. Using similar arguments, we define two new power indices. These new indices are defined taking into account only those winning coalitions that do not contain null players. The results obtained with the different power indices are compared by means of two real-world examples taken from the political field.
- 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.
- 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.
- Explosion of smoothness from a point to everywhere for conjugacies between Markov familiesPublication . Ferreira, Flávio; Pinto, Alberto A.For uniformly asymptotically affine (uaa) Markov maps on train tracks, we prove the following type of rigidity result: if a topological conjugacy between them is (uaa) at a point in the train track then the conjugacy is (uaa) everywhere. In particular, our methods apply to the case in which the domains of the Markov maps are Canter sets. We also present similar statements for (uaa:) and C-r Markov families. These results generalize the similar ones of Sullivan and de Faria for C-r expanding circle maps with r > 1 and have useful applications to hyperbolic dynamics on surfaces and laminations.