HOMEOMORPHISMS OF THE ANNULUS WITH A TRANSITIVE LIFT II

Let f be a homeomorphism of the closed annulus A that preserves the orientation, the boundary components and that has a lift (f) over tilde to the in finite strip (A) over tilde which is transitive. We show that, if the rotation number of (f) over tilde restricted to both boundary components of A is strictly positive, then there exists a closed nonempty connected set Gamma subset of (A) over tilde such that Gamma subset of] - infinity,0] x [0,1], Gamma is unbounded, the projection of to Gamma A is dense, Gamma - (1, 0) subset of Gamma and (f) over tilde(Gamma) subset of Gamma. Also, if p(1) is the projection on the first coordinate of (A) over tilde, then there exists d > 0 such that, for any (z) over tilde is an element of Gamma, lim sup (n ->infinity) p(1)((f) over tilde (n) ((Z) over tilde)) - p(1) ((Z) over tilde)/n < -d.

SUPPORT OF MAXIMIZING MEASURES FOR TYPICAL C(0) DYNAMICS ON COMPACT MANIFOLDS

Given a compact manifold X, a continuous function g : X -> IR, and a map T : X -> X, we study properties of the T-invariant Borel probability measures that maximize the integral of g. We show that if X is a n-dimensional connected Riemaniann manifold, with n >= 2, then the set of homeomorphisms for which there is a maximizing measure supported on a periodic orbit is meager. We also show that, if X is the circle, then the ""topological size"" of the set of endomorphisms for which there are g maximizing measures with support on a periodic orbit depends on properties of the function g. In particular, if g is C(1), it has interior points.

A DISCRETIZATION SCHEME FOR AN ONE-DIMENSIONAL REACTION-DIFFUSION EQUATION WITH DELAY AND ITS DYNAMICS

The goal of this paper is to present an approximation scheme for a reaction-diffusion equation with finite delay, which has been used as a model to study the evolution of a population with density distribution u, in such a way that the resulting finite dimensional ordinary differential system contains the same asymptotic dynamics as the reaction-diffusion equation.

Fibonacci bimodal maps

We introduce the Fibonacci bimodal maps on the interval and show that their two turning points are both in the same minimal invariant Cantor set. Two of these maps with the same orientation have the same kneading sequences and, among bimodal maps without central returns, they exhibit turning points with the strongest recurrence as possible.

A full family of multimodal maps on the circle

We exhibit a family of trigonometric polynomials inducing a family of 2m-multimodal maps on the circle which contains all relevant dynamical behavior.

CONTINUITY OF GLOBAL ATTRACTORS FOR A CLASS OF NON LOCAL EVOLUTION EQUATIONS

In this work we prove that the global attractors for the flow of the equation partial derivative m(r, t)/partial derivative t = -m(r, t) + g(beta J * m(r, t) + beta h), h, beta >= 0, are continuous with respect to the parameters h and beta if one assumes a property implying normal hyperbolicity for its (families of) equilibria.

NONSTATIONARY MIXING AND THE UNIQUE ERGODICITY OF ADIC TRANSFORMATIONS

We define topological and measure-theoretic mixing for nonstationary dynamical systems and prove that for a nonstationary subshift of finite type, topological mixing implies the minimality of any adic transformation defined on the edge space, while if the Parry measure sequence is mixing, the adic transformation is uniquely ergodic. We also show this measure theoretic mixing is equivalent to weak ergodicity of the edge matrices in the sense of inhomogeneous Markov chain theory.

Henon-like maps with arbitrary stationary combinatorics

We extend the renormalization operator introduced in [A. de Carvalho, M. Martens and M. Lyubich. Renormalization in the Henon family, I: universality but non-rigidity. J. Stat. Phys. 121(5/6) (2005), 611-669] from period-doubling Henon-like maps to Henon-like maps with arbitrary stationary combinatorics. We show that the renonnalization picture also holds in this case if the maps are taken to be strongly dissipative. We study infinitely renormalizable maps F and show that they have an invariant Cantor set O on which F acts like a p-adic adding machine for some p > 1. We then show, as for the period-doubling case in the work of de Carvalho, Martens and Lyubich [Renormalization in the Henon family, I: universality but non-rigidity. J. Stat. Phys. 121(5/6) (2005), 611-669], that the sequence of renormalizations has a universal form, but that the invariant Cantor set O is non-rigid. We also show that O cannot possess a continuous invariant line field.

Stabilizing Nonstationary Electrochemical Time Series

Electrochemical systems are ideal working-horses for studying oscillatory dynamics. Experimentally obtained time series, however, are usually associated with a spontaneous drift in some uncontrollable parameter that triggers transitions among different oscillatory patterns, despite the fact that all controllable parameters are kept constant. Herein we present an empirical method to stabilize experimental potential time series. The method consists of applying a negative galvanodynamic sweep to compensate the spontaneous drift and was tested for the oscillatory electro-oxidation of methanol on platinum. For a wide range of applied currents, the base system presents spontaneous transitions from quasi-harmonic to mixed mode oscillations. Temporal patterns were stabilized by galvanodynamic sweeps at different rates. The procedure resulted in a considerable increase in the number of oscillatory cycles from 5 to 20 times, depending on the specific temporal pattern. The spontaneous drift has been associated with uncompensated oscillations, in which the coverage of some adsorbed species are not reestablished after one cycle; i.e., there is a net accumulation and/or depletion of adsorbed species during oscillations. We interpreted the rate of the galvanodynamic sweep in terms of the time scales of the poisoning processes that underlies the uncompensated oscillations and thus the spontaneous slow drift.

On 3-Parameter Families of Piecewise Smooth Vector Fields in the Plane

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

Short Lyapunov time: a method for identifying confined chaos

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Optimal placement of piezoelectric sensor/actuators for smart structures vibration control

Smart material technology has become an area of increasing interest for the development of lighter and stronger structures that are able to incorporate actuator and sensor capabilities for collocated control. In the design of actively controlled structures, the determination of the actuator locations and the controller gains is a very important issue. For that purpose, smart material modeling, modal analysis methods, and control and optimization techniques are the most important ingredients to be taken into account. The optimization problem to be solved in this context presents two interdependent aspects. The first is related to the discrete optimal actuator location selection problem, which is solved in this paper using genetic algorithms. The second is represented by a continuous variable optimization problem, through which the control gains are determined using classical techniques. A cantilever Euler-Bernoulli beam is used to illustrate the presented methodology.

Processo de difusão com agregação e reorganização espontânea em uma rede 2D

Difusive processes are extremely common in Nature. Many complex systems, such as microbial colonies, colloidal aggregates, difusion of fluids, and migration of populations, involve a large number of similar units that form fractal structures. A new model of difusive agregation was proposed recently by Filoche and Sapoval [68]. Based on their work, we develop a model called Difusion with Aggregation and Spontaneous Reorganization . This model consists of a set of particles with excluded volume interactions, which perform random walks on a square lattice. Initially, the lattice is occupied with a density p = N/L2 of particles occupying distinct, randomly chosen positions. One of the particles is selected at random as the active particle. This particle executes a random walk until it visits a site occupied by another particle, j. When this happens, the active particle is rejected back to its previous position (neighboring particle j), and a new active particle is selected at random from the set of N particles. Following an initial transient, the system attains a stationary regime. In this work we study the stationary regime, focusing on scaling properties of the particle distribution, as characterized by the pair correlation function ø(r). The latter is calculated by averaging over a long sequence of configurations generated in the stationary regime, using systems of size 50, 75, 100, 150, . . . , 700. The pair correlation function exhibits distinct behaviors in three diferent density ranges, which we term subcritical, critical, and supercritical. We show that in the subcritical regime, the particle distribution is characterized by a fractal dimension. We also analyze the decay of temporal correlations

Non-lacunary Gibbs Measures for Certain Fractal Repellers

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)