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Browsing ESEIG - MAT - Artigos by Author "Ferreira, Flávio"
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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.
- 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.
- 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.
- 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.
- Flexibility in a Stackelberg leadership with differentiated goodsPublication . Ferreira, Fernanda A.; Ferreira, Flávio; Ferreira, Miguel; Pinto, Alberto A.We study the effects of product differentiation in a Stackelberg model with demand uncertainty for the first mover. We do an ex-ante and ex-post analysis of the profits of the leader and of the follower firms in terms of product differentiation and of the demand uncertainty. We show that even with small uncertainty about the demand, the follower firm can achieve greater profits than the leader, if their products are sufficiently differentiated. We also compute the probability of the second firm having higher profit than the leading firm, subsequently showing the advantages and disadvantages of being either the leader or the follower firm.
- 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.
- Licensing endogenous cost-reduction in a differentiated Stackelberg modelPublication . Ferreira, Flávio; Bode, Oana R.In this paper we consider a differentiated Stackelberg model, when the leader firm engages in an R&D process that gives an endogenous cost-reducing innovation. The aim is to study the licensing of the cost-reduction by a two-part tariff. By using comparative static analysis, we conclude that the degree of the differentiation of the goods plays an important role in the results. We also do a direct comparison between our model and Cournot duopoly model.