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- 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.
- 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.
- 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.
- 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.
- Hausdorff dimension bounds for smoothness of holonomies for codimension 1 hyperbolic dynamicsPublication . Pinto, Alberto A.; Rand, David A.; Ferreira, FlávioWe prove that the stable holonomies of a proper codimension 1 attractor Λ, for a Cr diffeomorphism f of a surface, are not C1+θ for θ greater than the Hausdorff dimension of the stable leaves of f intersected with Λ. To prove this result we show that there are no diffeomorphisms of surfaces, with a proper codimension 1 attractor, that are affine on a neighbourhood of the attractor and have affine stable holonomies on the attractor.
- Equilíbrio de Nash versus Óptimo de Pareto: racionalidade individualista versus racionalidade altruístaPublication . Ferreira, Fernanda A.; Ferreira, Flávio
- Maximum-revenue tariff under Bertrand duopoly with unknown costsPublication . Ferreira, Fernanda A.; Ferreira, FlávioThis paper considers an international trade under Bertrand model with differentiated products and with unknown production costs. The home government imposes a specific import tariff per unit of imports from the foreign firm. We prove that this tariff is decreasing in the expected production costs of the foreign firm and increasing in the production costs of the home firm. Furthermore, it is increasing in the degree of product substitutability. We also show that an increase in the tariff results in both firms increasing their prices, an increase in both expected sales and expected profits for the home firm, and a decrease in both expected sales and expected profits for the foreign firm.
- Minimization of open orders using interval graphsPublication . Lopes, Isabel Cristina; Carvalho, J. M. Valerio deIn this paper we address an order processing optimization problem known as the Minimization of Open Stacks Problem (MOSP). This problem consists in finding the best sequence for manufacturing the different products required by costumers, in a setting where only one product can be made at a time. The objective is to minimize the maximum number of incomplete orders from costumers that are being processed simultaneously. We present an integer programming model, based on the existence of a perfect elimination order in interval graphs, which finds an optimal sequence for the costumers orders. Among other economic advantages, manufacturing the products in this optimal sequence reduces the amount of space needed to store incomplete orders.
- 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.