Hausdorff dimension of non-hyperbolic repellers. I: Maps with holes

This is the first paper in a two-part series devoted to studying the Hausdorff dimension of invariant sets of non-uniformly hyperbolic, non-conformal maps. Here we consider a general abstract model, that we call piecewise smooth maps with holes. We show that the Hausdorff dimension of the repeller is strictly less than the dimension of the ambient manifold. Our approach also provides information on escape rates and dynamical dimension of the repeller.

Hausdorff dimension for non-hyperbolic repellers II: Da diffeomorphisms

We study non-hyperbolic repellers of diffeomorphisms derived from transitive Anosov diffeomorphisms with unstable dimension 2 through a Hopf bifurcation. Using some recent abstract results about non-uniformly expanding maps with holes, by ourselves and by Dysman, we show that the Hausdorff dimension and the limit capacity (box dimension) of the repeller are strictly less than the dimension of the ambient manifold.

Estimativas inferiores para dimensão de Hausdorff de repulsores não-uniformemente expansores

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

A crítica de Mandelbrot: normalidade como exceção e não como regra

Starting with a brief introduction about the evolution of asset pricing models, we seek here to introduce the critique made by Benoit Mandelbrot about using the normality hypothesis when building such models. This critique arises when empirical and theoretical models where confronted and the expected results diverged from the ones obtained. Next, we reproduce Mandelbrot alternative which he believes is sufficient to solve the main problems implied by the normality hyphotesis

Sparse one-dimensional discrete Dirac operators II: Spectral properties

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

Comments about some species abundance patterns: classic, neutral, and niche partitioning models

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

On turbulent, erratic and other dynamical properties of Zadeh's extensions

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

Singular perturbation problems for time-reversible systems

In this paper singularly perturbed reversible vector fields defined in R-n without normal hyperbolicity conditions are discussed. The main results give conditions for the existence of infinitely many periodic orbits and heteroclinic cycles converging to singular orbits with respect to the Hausdorff distance.

Limit cycles for singular perturbation problems via inverse integrating factor

In this paper singularly perturbed vector fields Xε defined in ℝ2 are discussed. The main results use the solutions of the linear partial differential equation XεV = div(Xε)V to give conditions for the existence of limit cycles converging to a singular orbit with respect to the Hausdorff distance. © SPM.

Chaos induced by turbulent and erratic functions

Let (X, d) be a compact metric space and f: X → X a continuous function and consider the hyperspace (K(X), H) of all nonempty compact subsets of X endowed with the Hausdorff metric induced by d. Let f̄: K(X) → K (X) be defined by f̄(A) = {f(a)/a ∈ A} the natural extension of f to K(X), then the aim of this work is to study the dynamics of f when f is turbulent (erratic, respectively) and its relationships.

Análise espaço temporal da dimensão fractal de matas ciliares na alta bacia do rio Passa Cinco - centro Leste do Estado de São Paulo

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

Propriedades topológicas dos conjuntos de Julia

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Propriedades topológicas e aritméticas dos fractais de Rauzy

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Aplicação de análise fractal em rede de drenagem e relevo de bacias hidrográficas de terceira ordem de ramificação

Pós-graduação em Agronomia (Energia na Agricultura) - FCA

Propriedades espectrais uniformes para operadores de Schrödinger com potenciais Sturmianos

Pós-graduação em Matematica Aplicada e Computacional - FCT