Browsing by Author "Carvalho, Maria"
Now showing 1 - 7 of 7
Results Per Page
Sort Options
- Frisos imperfeitos de números inteirosPublication . Bessa, Mário; Carvalho, MariaA positive density ensures not only that the set is infinite but also that the arrangement of its elements is such that it is possible to find inside it highly symmetric and arbitrarily long blocks of equidistant points. For example, although this is not a necessary condition [1, 4], a set N with positive density must include arbitrarily long arithmetic progressions [3, 2]. That is, given a positive integer k, there are positive integers a,b such that a+jb ∈ N , for all j ∈ {0,...,k}. However, no information is given about the ratio b in the arithmetical progression, and surely not all choices of b are suitable for a fixed set. Nevertheless, a positive density set has to contain, up to an arbitrarily small error, a scaled copy of any finite block of rational numbers of [0, 1], for all scales not bigger than a specified bound.
- Generic area-preserving reversible diffeomorphismsPublication . Bessa, Mário; Carvalho, Maria; Rodrigues, Alexandre A. P.Let M be a surface and R : M → M an area-preserving C∞ diffeomorphism which is an involution and whose set of fixed points is a submanifold with dimension one. We will prove that C1 -generically either an area-preserving R-reversible diffeomorphism, is Anosov, or, for μ-almost every x ∈ M, the Lyapunov exponents at x vanish or else the orbit of x belongs to a compact hyperbolic set with an empty interior. We will also describe a nonempty C1- open subset of area-preserving R-reversible diffeomorphisms where for C1-generically each map is either Anosov or its Lyapunov exponents vanish from almost everywhere.
- Non-uniform hyperbolicity for infinite dimensional cocyclesPublication . Bessa, Mário; Carvalho, MariaLet H be an infinite dimensional separable Hilbert space, X a compact Hausdorff space and f : X \rightarrow X a homeomorphism which preserves a Borel ergodic measure which is positive on non-empty open sets. We prove that the non-uniformly Anosov cocycles are C0-dense in the family of partially hyperbolic f,H-skew products with non-trivial unstable bundles.
- A note on reversibility and Pell equationsPublication . Bessa, Mário; Carvalho, Maria; Rodrigues, Alexandre A. P.This note concerns hyperbolic toral automorphisms which are reversible with respect to a linear area-preserving involution. Due to the low dimension, we will be able to associate the reversibility with a generalized Pell equation from whose set of solutions we will infer further information. Additionally, we will show that reversibility is a rare feature and will characterize the generic setting.
- On the Lyapunov spectrum of infinite dimensional random products of compact operatorsPublication . Bessa, Mário; Carvalho, MariaWe consider an infinite dimensional separable Hilbert space and its family of compact integrable cocycles over a dynamical system f. Assuming that f acts in a compact Hausdorff space X and preserves a Borel regular ergodic probability which is positive on non-empty open sets, we conclude that there is a C0-residual subset of cocycles within which, for almost every x, either the Oseledets–Ruelle’s decomposition along the orbit of x is dominated or all the Lyapunov exponents are equal to −∞.
- The impact of e-commerce on the success of microenterprise retail sector of the Pinhal Interior Norte sub-region of PortugalPublication . Carvalho, Maria; São Mamede, HenriqueIn the global, competitive and ever-changing market it is important that Micro, Small and Medium Enterprises (MSME), as a significant part of the Portuguese industrial business, become competitive and, thus, it ́s important to assess how the level of involvement in Electronic Commerce (EC), in Business-to-Consumer (B2C) relations, can influence the success of a microenterprise in the retail sector, focusing on the Portuguese sub-region of Pinhal Interior Norte. Being a region that is far from the big metropolises, where the young and more educated stratum distances itself, leaving it little more than the population that is getting older and with a reduced level of education, we considered it interesting to study if the microenterprises of the region are prepared to the new era of technology as a business model for their companies. Using the definition of success for a company as positive and growing financial result, it is objective of this work to know if companies with involvement in the EC, in B2C relations, have an increasing success rate due to its adoption and maintenance. Based on a research in a database with information from the companies, the sample was subsequently evaluated to find out which of the companies in the sample were involved in the EC and conducted surveys / interviews with the managers of the sample companies to assess the motivation (s) for their adoption, as well as whether they recognize the return of their investment and what they intend to do to maintain or modify their business. Initially we found several difficulties to gather data to be able to achieve proper conclusions, but with the help of some company managers, we were able to confirm that 62.50% of the analyzed companies saw their financial result increased after the adoption of the EC, which allows us to establish the existence of a relationship between the two facts.
- The role of the saddle-foci on the structure of a bykov attracting setPublication . Bessa, Mário; Carvalho, Maria; Rodrigues, Alexandre A. P.We consider a one-parameter family ( fλ)λ 0 of symmetric vector fields on the three-dimensional sphere whose flows exhibit a heteroclinic network between two saddle-foci inside a global attracting set. More precisely, when λ = 0, there is an attracting heteroclinic cycle between the two equilibria which is made of two 1- dimensional connections together with a 2-dimensional sphere which is both the stable manifold of one saddle-focus and the unstable manifold of the other. After slightly increasing the parameter while keeping the 1-dimensional connections unaltered, the two-dimensional invariant manifolds of the equilibria become transversal, and thereby create homoclinic and heteroclinic tangles. It is known that these newborn structures are the source of a countable union of topological horseshoes, which prompt the coexistence of infinitely many sinks and saddle-type invariant sets for many values of λ. We show that, for every small enough positive parameter λ, the stable and unstable manifolds of the saddle-foci and those infinitely many horseshoes are contained in the global attracting set of fλ; moreover, the horseshoes belong to the heteroclinic class of the equilibria. In addition, we show that the set of chain-accessible points from either of the saddle-foci is chain-stable and contains the closure of the invariant manifolds of the two equilibria.