A rescaling of the phase space for Hamiltonian map: Applications on the Kepler map and mappings with diverging angles in the limit of vanishing action

A rescale of the phase space for a family of two-dimensional, nonlinear Hamiltonian mappings was made by using the location of the first invariant Kolmogorov-Arnold-Moser (KAM) curve. Average properties of the phase space are shown to be scaling invariant and with different scaling times. Specific values of the control parameters are used to recover the Kepler map and the mapping that describes a particle in a wave packet for the relativistic motion. The phase space observed shows a large chaotic sea surrounding periodic islands and limited by a set of invariant KAM curves whose position of the first of them depends on the control parameters. The transition from local to global chaos is used to estimate the position of the first invariant KAM curve, leading us to confirm that the chaotic sea is scaling invariant. The different scaling times are shown to be dependent on the initial conditions. The universality classes for the Kepler map and mappings with diverging angles in the limit of vanishing action are defined. © 2013 Published by Elsevier Inc. All rights reserved.

Límite de la responsabilidad civil del porteador en el transporte terrestre internacional en América Latina: criterios para su fijación = Limit of civil liability of carriers in international land transport in Latin America: criteria for its establishment

Incluye Bibliografía

Birth of limit cycles bifurcating from a nonsmooth center

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

Control of Limit Cycle Oscillation in a Three Degrees of Freedom Airfoil Section Using Fuzzy Takagi-Sugeno Modeling

This work presents a strategy to control nonlinear responses of aeroelastic systems with control surface freeplay. The proposed methodology is developed for the three degrees of freedom typical section airfoil considering aerodynamic forces from Theodorsen's theory. The mathematical model is written in the state space representation using rational function approximation to write the aerodynamic forces in time domain. The control system is designed using the fuzzy Takagi-Sugeno modeling to compute a feedback control gain. It useds Lyapunov's stability function and linear matrix inequalities (LMIs) to solve a convex optimization problem. Time simulations with different initial conditions are performed using a modified Runge-Kutta algorithm to compare the system with and without control forces. It is shown that this approach can compute linear control gain able to stabilize aeroelastic systems with discontinuous nonlinearities.

Limit Cycles for a Class of Continuous and Discontinuous Cubic Polynomial Differential Systems

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Dimensional reduction of the massless limit of the linearized 'New Massive Gravity'

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Trimer-Tetramer Interwoven States in the Scaling Limit

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

Limit cycles of cubic polynomial differential systems with rational first integrals of degree 2

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

On the number of limit cycles in discontinuous piecewise linear differential systems with two pieces separated by a straight line

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

On the Limit Cycles for a Class of Continuous Piecewise Linear Differential Systems with Three Zones

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

Limit on the pion distribution amplitude

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Glycerol combined with oils did not limit biohydrogenation of unsaturated fatty acid but reduced methane production in vitro

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

Infinite tension limit of the pure spinor superstring

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Type 0 open string amplitudes and the tensionless limit

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

Local order and magnetic field effects on the electronic properties of disordered binary alloys in the quantum site percolation limit

Electronic properties of disordered binary alloys are studied via the calculation of the average Density of States (DOS) in two and three dimensions. We propose a new approximate scheme that allows for the inclusion of local order effects in finite geometries and extrapolates the behavior of infinite systems following finite-size scaling ideas. We particularly investigate the limit of the Quantum Site Percolation regime described by a tight-binding Hamiltonian. This limit was chosen to probe the role of short range order (SRO) properties under extreme conditions. The method is numerically highly efficient and asymptotically exact in important limits, predicting the correct DOS structure as a function of the SRO parameters. Magnetic field effects can also be included in our model to study the interplay of local order and the shifted quantum interference driven by the field. The average DOS is highly sensitive to changes in the SRO properties and striking effects are observed when a magnetic field is applied near the segregated regime. The new effects observed are twofold: there is a reduction of the band width and the formation of a gap in the middle of the band, both as a consequence of destructive interference of electronic paths and the loss of coherence for particular values of the magnetic field. The above phenomena are periodic in the magnetic flux. For other limits that imply strong localization, the magnetic field produces minor changes in the structure of the average DOS. © World Scientific Publishing Company.