Paper surfaces and dynamical limits

It is very common in mathematics to construct surfaces by identifying the sides of a polygon together in pairs: For example, identifying opposite sides of a square yields a torus. In this article the construction is considered in the case where infinitely many pairs of segments around the boundary of the polygon are identified. The topological, metric, and complex structures of the resulting surfaces are discussed: In particular, a condition is given under which the surface has a global complex structure (i.e., is a Riemann surface). In this case, a modulus of continuity for a uniformizing map is given. The motivation for considering this construction comes from dynamical systems theory: If the modulus of continuity is uniform across a family of such constructions, each with an iteration defined on it, then it is possible to take limits in the family and hence to complete it. Such an application is briefly discussed.

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.

PERIODIC PERTURBATION of QUADRATIC SYSTEMS WITH TWO INFINITE HETEROCLINIC CYCLES

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Effect of cosurfactant on the supramolecular structure and physicochemical properties of non-ionic biocompatible microemulsions

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

Wigner distribution for a class of isospectral position-dependent mass systems

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Stabilizing controller design for uncertain nonlinear systems using fuzzy models

A Lyapunov-based stabilizing control design method for uncertain nonlinear dynamical systems using fuzzy models is proposed. The controller is constructed using a design model of the dynamical process to be controlled. The design model is obtained from the truth model using a fuzzy modeling approach. The truth model represents a detailed description of the process dynamics. The truth model is used in a simulation experiment to evaluate the performance of the controller design. A method for generating local models that constitute the design model is proposed. Sufficient conditions for stability and stabilizability of fuzzy models using fuzzy state-feedback controllers are given. The results obtained are illustrated with a numerical example involving a four-dimensional nonlinear model of a stick balancer.

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.

On a control of a non-ideal mono-rail system with periodics coefficients

In this work, the problem in the loads transport (in platforms or suspended by cables) it is considered. The system in subject is composed for mono-rail system and was modeled through the system: inverted pendulum, car and motor and the movement equations were obtained through the Lagrange equations. In the model, was considered the interaction among of the motor and system dynamics for several potencies motor, that is, the case studied is denominated a non-ideal periodic problem. The non-ideal periodic problem dynamics was analyzed, qualitatively, through the comparison of the stability diagrams, numerically obtained, for several motor torque constants. Furthermore, one was made it analyzes quantitative of the problem through the analysis of the Floquet multipliers. Finally, the non-ideal problem was controlled. The method that was used for analysis and control of non-ideal periodic systems is based on the Chebyshev polynomial expansion, in the Picard iterative method and in the Lyapunov-Floquet transformation (L-F trans formation). This method was presented recently in [3-9].

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.

OUTPUT CONTROL WITH DYNAMIC COMPENSATORS AND STRICTLY POSITIVE REAL SYSTEMS

We present new results on the output control of uncertain dynamical systems. The design method uses dynamical compensators to turn the compensated plant into a strictly positive real system, and then chooses the control law-for example, a sliding mode control. This result is compared with another result from the literature which uses static compensators. An example is presented where the control with dynamic compensation works while a static compensation does not.

Stability for impulsive control systems

In this paper we extend the notion of the control Lyapounov pair of functions and derive a stability theory for impulsive control systems. The control system is a measure driven differential inclusion that is partly absolutely continuous and partly singular. Some examples illustrating the features of Lyapounov stability are provided.

Local dimension and finite time prediction in spatiotemporal chaotic systems

Predictability is related to the uncertainty in the outcome of future events during the evolution of the state of a system. The cluster weighted modeling (CWM) is interpreted as a tool to detect such an uncertainty and used it in spatially distributed systems. As such, the simple prediction algorithm in conjunction with the CWM forms a powerful set of methods to relate predictability and dimension.

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.

A structure excited by a DC motor of limited power supply and controlled by a pendulum like device

In this paper, a mathematical model is derived via Lagrange's Equation for a shear building structure that acts as a foundation of a non-ideal direct current electric motor, controlled by a mass loose inside a circular carving. Non-ideal sources of vibrations of structures are those whose characteristics are coupled to the motion of the structure, not being a function of time only as in the ideal case. Thus, in this case, an additional equation of motion is written, related to the motor rotation, coupled to the equation describing the horizontal motion of the shear building. This kind of problem can lead to the so-called Sommerfeld effect: steady state frequencies of the motor will usually increase as more power (voltage) is given to it in a step-by-step fashion. When a resonance condition with the structure is reached, the better part of this energy is consumed to generate large amplitude vibrations of the foundation without sensible change of the motor frequency as before. If additional increase steps in voltage are made, one may reach a situation where the rotor will jump to higher rotation regimes, no steady states being stable in between. As a device of passive control of both large amplitude vibrations and the Sommerfeld effect, a scheme is proposed using a point mass free to bounce back and forth inside a circular carving in the suspended mass of the structure. Numerical simulations of the model are also presented Copyright © 2007 by ASME.

On the analytical solution for the slewing flexible beam-like system: analysis of the linear part of the perturbed problem

The dynamical system investigated in this work is a nonlinear flexible beam-like structure in slewing motion. Non-dimensional and perturbed governing equations of motion are presented. The analytical solution for the linear part of these perturbed equations for ideal and for non-ideal cases are obtained. This solution is necessary for the investigation of the complete weak nonlinear problem where all nonlinearities are small perturbations around a linear known solution. This investigation shall help the analyst in the modelling of dynamical systems with structure- actuator interactions.