Non-lacunary Gibbs Measures for Certain Fractal Repellers

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Time series analysis for minority game simulations of financial markets

The minority game (MG) model introduced recently provides promising insights into the understanding of the evolution of prices, indices and rates in the financial markets. In this paper we perform a time series analysis of the model employing tools from statistics, dynamical systems theory and stochastic processes. Using benchmark systems and a financial index for comparison, several conclusions are obtained about the generating mechanism for this kind of evolution. The motion is deterministic, driven by occasional random external perturbation. When the interval between two successive perturbations is sufficiently large, one can find low dimensional chaos in this regime. However, the full motion of the MG model is found to be similar to that of the first differences of the SP500 index: stochastic, nonlinear and (unit root) stationary. (C) 2002 Elsevier B.V. B.V. All rights reserved.

Transition to turbulence in the Reynolds' experiment

In this study we simulate numerically the Reynolds' experiment for the transition from laminar to turbulent flow in a pipe. We present a discussion of the results from a dynamical systems perspective when a control parameter, the Reynolds number, is increased. The Landau scenario, where the transition is described by the excitation of infinite oscillatory modes within the fluid, is not observed. Instead what happens is best explained by the Ruelle-Takens scenario in terms of strange attractors. The Lyapunov exponent and fractal dimension for the attractor are calculated together with a measure of complex behaviour called the Lempel-Ziv complexity. (C) 2001 Elsevier B.V. B.V. All rights reserved.

Brane cosmic string compactification in Brans-Dicke theory

We investigate an alternative compactification of extra dimensions using local cosmic string in the Brans-Dicke gravity framework. In the context of dynamical systems it is possible to show that there exist a stable field configuration for the Einstein-Brans-Dicke equations. We explore the analogies between this particular model and the Randall-Sundrum scenario.

Transition to complete synchronization in phase-coupled oscillators with nearest neighbor coupling

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

A review of new vibration issues due to non-ideal energy sources

We analyze the dynamical coupling between energy sources and structural response that must not be ignored in real engineering problems, since real motors have limited output power. We present models of certain problems that render descriptions that are closer to real situations encountered in practice.

Control and chaos for vibro-impact and non-ideal oscillators

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

Escape and transport for an open bouncer: Stretched exponential decays

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Dissipation as a mechanism of energy gain

Some properties of the annular billiard under the presence of weak dissipation are studied. We show, in a dissipative system, that the average energy of a particle acquires higher values than its average energy of the conservative case. The creation of attractors, associated with a chaotic dynamics in the conservative regime, both in appropriated regions of the phase space, constitute a generic mechanism to increase the average energy of dynamical systems.

Divergent diagrams of folds and simultaneous conjugacy of involutions

In this work we show that the smooth classification of divergent diagrams of folds (f(1),..., f(s)) : (R-n, 0) -> (R-n x(...)xR(n), 0) can be reduced to the classification of the s-tuples (p(1)., W) of associated involutions. We apply the result to obtain normal forms when s <= n and {p(1),...,p(s)} is a transversal set of linear involutions. A complete description is given when s = 2 and n >= 2. We also present a brief discussion on applications of our results to the study of discontinuous vector fields and discrete reversible dynamical systems.

VERY RAPIDLY VARYING BOUNDARIES IN EQUATIONS WITH NONLINEAR BOUNDARY CONDITIONS. THE CASE of A NON UNIFORMLY LIPSCHITZ DEFORMATION

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

Percepção e ação: direções teóricas e experimentais atuais

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

An examination of constraints affecting the intralimb coordination of hemiparetic gait

A dynamical systems approach to the study of locomotor intralimb coordination in those with hemiparesis led to an examination of the utility of the shank-thigh relative phase (RP) as a collective variable and the identification of potential constraints that may shape this coordination. Eighteen non-disabled individuals formed three groups matched to the age and gender of six participants with chronic right hemiparesis. The three groups differed in the constraints imposed on their walking: (1) walking at their preferred walking speed; (2) walking as slowly as those with hemiparesis; and, (3) walking slowly with a right ankle-foot orthosis (AFO). The results revealed an asymmetry in intralimb coordination between the unaffected and affected leg of those with hemiparesis localized to the latter third of the gait cycle when the limb is advanced from the end of stance to the reestablishment of a new stance. Walking slowly with or without an AFO resulted in no measureable effect in the non-disabled, but accounts for 22% of the variance in the intralimb coordination of the hemiplegic's affected limb and 16% in the unaffected limb. The AFO offered little additional contribution. These results derive from shank-thigh RP that is shown to provide more information about intralimb coordination than knee angle displacement. Implications for these results and the use of RP for rehabilitation are discussed. (C) 2000 Elsevier B.V. B.V. All rights reserved. PsycINFO classification. 3297. 2330.

Effects of the eccentricity on the primaries in the gravitational capture phenomenon

Gravitational capture is a characteristic of some dynamical systems in celestial mechanics, as in the elliptic restricted three-body problem that is considered in this paper. The basic idea is that a spacecraft (or any particle with negligible mass) can change a hyperbolic orbit with a small positive energy around a celestial body into an elliptic orbit with a small negative energy without the use of any propulsive system. The force responsible for this modification in the orbit of the spacecraft is the gravitational force of the third body involved in the dynamics. In this way, this force is used as a zero cost control, equivalent to a continuous thrust applied in the spacecraft. One of the most important applications of this property is the construction of trajectories to the Moon. The objective of the present paper is to study in some detail the effects of the eccentricity of the primaries in this maneuver.