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.

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.

Non-periodic bifurcations of one-dimensional maps

We prove that a 'positive probability' subset of the boundary of '{uniformly expanding circle transformations}' consists of Kupka-Smale maps. More precisely, we construct an open class of two-parameter families of circle maps (f(alpha,theta))(alpha,theta) such that, for a positive Lebesgue measure subset of values of alpha, the family (f(alpha,theta))(theta) crosses the boundary of the uniformly expanding domain at a map for which all periodic points are hyperbolic (expanding) and no critical point is pre-periodic. Furthermore, these maps admit an absolutely continuous invariant measure. We also provide information about the geometry of the boundary of the set of hyperbolic maps.

Bifurcation of limit cycles from a centre in R-4 in resonance 1:N

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

Strategies for plane change of Earth orbits using lunar gravity and derived trajectories of family G

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

Fermi acceleration and scaling properties of a time dependent oval billiard

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Reversible Hamiltonian Liapunov center theorem

We study the existence of periodic solutions in the neighbourhood of symmetric (partially) elliptic equilibria in purely reversible Hamiltonian vector fields. These are Hamiltonian vector fields with an involutory reversing symmetry R. We contrast the cases where R acts symplectically and anti-symplectically. In case R acts anti-symplectically, generically purely imaginary eigenvalues are isolated, and the equilibrium is contained in a local two-dimensional invariant manifold containing symmetric periodic solutions encircling the equilibrium point. In case R acts symplectically, generically purely imaginary eigenvalues are doubly degenerate, and the equilibrium is contained in two two-dimensional invariant manifolds containing nonsymmetric periodic solutions encircling the equilibrium point. In addition, there exists a three-dimensional invariant surface containing a two-parameter family of symmetric periodic solutions.

Local dimension and finite time prediction in coupled map lattices

Forecasting, for obvious reasons, often become the most important goal to be achieved. For spatially extended systems (e.g. atmospheric system) where the local nonlinearities lead to the most unpredictable chaotic evolution, it is highly desirable to have a simple diagnostic tool to identify regions of predictable behaviour. In this paper, we discuss the use of the bred vector (BV) dimension, a recently introduced statistics, to identify the regimes where a finite time forecast is feasible. Using the tools from dynamical systems theory and Bayesian modelling, we show the finite time predictability in two-dimensional coupled map lattices in the regions of low BV dimension. © Indian Academy of Sciences.

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.

Information and mechanical models of intelligence: What can we learn from cognitive science?

The impact of new advanced technology on issues that concern meaningful information and its relation to studies of intelligence constitutes the main topic of the present paper. The advantages, disadvantages and implications of the synthetic methodology developed by cognitive scientists, according to which mechanical models of the mind, such as computer simulations or self-organizing robots, may provide good explanatory tools to investigate cognition, are discussed. A difficulty with this methodology is pointed out, namely the use of meaningless information to explain intelligent behavior that incorporates meaningful information. In this context, it is inquired what are the contributions of cognitive science to contemporary studies of intelligent behavior and how technology may play a role in the analysis of the relationships established by organisms in their natural and social environments. © John Benjamins Publishing Company.

Effects of the eccentricity on the primames 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.

Basin problem for Hénon-like attractors in arbitrary dimensions

We prove that Hénon-like strange attractors of diffeomorphisms in any dimensions, such as considered in [2],[7], and [9] support a unique Sinai-Ruelle-Bowen (SRB) measure and have the no-hole property: Lebesgue almost every point in the basin of attraction is generic for the SRB measure. This extends two-dimensional results of Benedicks-Young [4] and Benedicks-Viana [3], respectively.