On Global Attractors for a Class of Parabolic Problems

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Conformal inflation from the Higgs

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Statistical properties for a dissipative model of relativistic particles in a wave packet: A parameter space investigation

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Controle de dissociação molecular com ferramentas de dinâmica não linear

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Crises de fronteira e estruturas complexas no espaço de parâmetros em um mapeamento dissipativo bidimensional

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Dynamics of a charged particle in a dissipative Fermi-Ulam model

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

A dissipative Fermi-Ulam model under two different kinds of dissipation

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Tópicos em teoria das perturbações cosmológicas

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Atratores pullback para equações parabólicas semilineares em domínios não cilíndricos

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Hiperbolicidade seccional em dimensões arbitrárias

Pós-graduação em Matemática - IBILCE

An extension of the invariance principle for dwell-time switched nonlinear systems

In this paper, we propose an extension of the invariance principle for nonlinear switched systems under dwell-time switched solutions. This extension allows the derivative of an auxiliary function V, also called a Lyapunov-like function, along the solutions of the switched system to be positive on some sets. The results of this paper are useful to estimate attractors of nonlinear switched systems and corresponding basins of attraction. Uniform estimates of attractors and basin of attractions with respect to time-invariant uncertain parameters are also obtained. Results for a common Lyapunov-like function and multiple Lyapunov-like functions are given. Illustrative examples show the potential of the theoretical results in providing information on the asymptotic behavior of nonlinear dynamical switched systems. (C) 2012 Elsevier B.V. All rights reserved.

Continuity of Dynamical Structures for Nonautonomous Evolution Equations Under Singular Perturbations

In this paper we study the continuity of invariant sets for nonautonomous infinite-dimensional dynamical systems under singular perturbations. We extend the existing results on lower-semicontinuity of attractors of autonomous and nonautonomous dynamical systems. This is accomplished through a detailed analysis of the structure of the invariant sets and its behavior under perturbation. We prove that a bounded hyperbolic global solutions persists under singular perturbations and that their nonlinear unstable manifold behave continuously. To accomplish this, we need to establish results on roughness of exponential dichotomies under these singular perturbations. Our results imply that, if the limiting pullback attractor of a nonautonomous dynamical system is the closure of a countable union of unstable manifolds of global bounded hyperbolic solutions, then it behaves continuously (upper and lower) under singular perturbations.

Continuity of Lyapunov functions and of energy level for generalized gradient semigroup

The global attractor of a gradient-like semigroup has a Morse decomposition. Associated to this Morse decomposition there is a Lyapunov function (differentiable along solutions)-defined on the whole phase space- which proves relevant information on the structure of the attractor. In this paper we prove the continuity of these Lyapunov functions under perturbation. On the other hand, the attractor of a gradient-like semigroup also has an energy level decomposition which is again a Morse decomposition but with a total order between any two components. We claim that, from a dynamical point of view, this is the optimal decomposition of a global attractor; that is, if we start from the finest Morse decomposition, the energy level decomposition is the coarsest Morse decomposition that still produces a Lyapunov function which gives the same information about the structure of the attractor. We also establish sufficient conditions which ensure the stability of this kind of decomposition under perturbation. In particular, if connections between different isolated invariant sets inside the attractor remain under perturbation, we show the continuity of the energy level Morse decomposition. The class of Morse-Smale systems illustrates our results.

An estimate on the fractal dimension of attractors of gradient-like dynamical systems

This paper is dedicated to estimate the fractal dimension of exponential global attractors of some generalized gradient-like semigroups in a general Banach space in terms of the maximum of the dimension of the local unstable manifolds of the isolated invariant sets, Lipschitz properties of the semigroup and the rate of exponential attraction. We also generalize this result for some special evolution processes, introducing a concept of Morse decomposition with pullback attractivity. Under suitable assumptions, if (A, A*) is an attractor-repeller pair for the attractor A of a semigroup {T(t) : t >= 0}, then the fractal dimension of A can be estimated in terms of the fractal dimension of the local unstable manifold of A*, the fractal dimension of A, the Lipschitz properties of the semigroup and the rate of the exponential attraction. The ingredients of the proof are the notion of generalized gradient-like semigroups and their regular attractors, Morse decomposition and a fine analysis of the structure of the attractors. As we said previously, we generalize this result for some evolution processes using the same basic ideas. (C) 2012 Elsevier Ltd. All rights reserved.

GALAXIES BEHIND THE GALACTIC PLANE: FIRST RESULTS AND PERSPECTIVES FROM THE VVV SURVEY

VISTA Variables in the Via Lactea (VVV) is an ESO variability survey that is performing observations in near-infrared bands (ZY JHK(s)) toward the Galactic bulge and part of the disk with the completeness limits at least 3 mag deeper than Two Micron All Sky Survey. In the present work, we searched in the VVV survey data for background galaxies near the Galactic plane using ZY JHK(s) photometry that covers 1.636 deg(2). We identified 204 new galaxy candidates by analyzing colors, sizes, and visual inspection of multi-band (ZY JHK(s)) images. The galaxy candidate colors were also compared with the predicted ones by star count models considering a more realistic extinction model at the same completeness limits observed by VVV. A comparison of the galaxy candidates with the expected one by Millennium simulations is also presented. Our results increase the number density of known galaxies behind the Milky Way by more than one order of magnitude. A catalog with galaxy properties including ellipticity, Petrosian radii, and ZY JHK(s) magnitudes is provided, as well as comparisons of the results with other surveys of galaxies toward the Galactic plane.