Showing papers in "Physica D: Nonlinear Phenomena in 1983"

TL;DR: In this paper, the correlation exponent v is introduced as a characteristic measure of strange attractors which allows one to distinguish between deterministic chaos and random noise, and algorithms for extracting v from the time series of a single variable are proposed.

TL;DR: In this article, it was shown that fractals in general and strange attractors in particular are characterized by an infinite number of generalized dimensions Dq, q > 0, which correspond to exponents associated with ternary, quaternary and higher correlation functions.

TL;DR: In this article, the authors show that crisis events are prevalent in many circumstances and systems, and that, just past a crisis, certain characteristic statistical behavior (whose type depends on the type of crisis) occurs.

TL;DR: In this paper, the authors discuss a variety of different definitions of dimension, compute their values for a typical example, and review previous work on the dimension of chaotic attractors, and conclude that dimension of the natural measure is more important than the fractal dimension.

TL;DR: In this paper, a semipopular account of the universal scaling theory for the period doubling route to chaos is presented, where the authors show that it can be seen as a form of a deterministic linear model.

TL;DR: A rigorous study of the ground states of one-dimensional models generalizing the discrete Frenkel-Kontorova model has been presented in this article, where the extremalization equations of the energy of these models turn out to define area preserving twist maps which exhibits periodic, quasi-periodic and chaotic orbits.

TL;DR: In this article, it was shown that Euler's equations are Lie-Poisson equations associated to the group of volume-preserving diffeomorphisms, and the dual of the Lie algebra is the space of vortices, and Kelvin's circulation theorem is interpreted as preservation of coadjoint orbits.

TL;DR: In this paper, the authors present new numerical and theoretical results concerning kink-antikink collisions in the classical φ 4 field model in one-dimensional space, and describe the results of a new high-precision computer simulation that significantly extends and refines these observations of escape windows.

TL;DR: In this article, the exact results on the discrete Frenkel-Kontorova (FK) model and its extensions have been reviewed and a series of rigorous upper bounds for the stochasticity threshold of the standard map were obtained.

TL;DR: In this article, the authors examined the effect of small stable regions or islands on the correlation function for the stochastic trajectories of the Hamiltonians of two degrees of freedom.

TL;DR: In this paper, two fixed points are found representing different types of universal behavior: a trivial fixed point for smooth motion and a nontrivial fixed point to represent the incipient breakup of a quasiperiodic motion with frequency ratio the golden mean into a more chaotic flow.

TL;DR: In this article, an exact renormalization group transformation is developed for dissipative systems which describes how the transition to chaos may occur in a continuous and universal manner if the frequency ratio in the quasi-periodic regime is held at a fixed irrational value.

TL;DR: In this paper, phase space portraits have been constructed and analyzed for noisy (nonperiodic) data obtained in an experiment on a nonequilibrium homogeneous chemical reaction, where phase space trajectories define a limit set that is an "attractor" - following a perturbation, the trajectory quickly returns to the attracting set.

TL;DR: In this paper, the authors investigate the effects of such fluctuations coupled to deterministic chaotic systems, in particular, the metric entropy's response to the fluctuations, and find that the entropy increases with a power law in the noise level, and that the convergence of the entropy and the effect of fluctuations can be cast as a scaling theory.

TL;DR: In this paper, a canonical Poisson bracket in the space of Clebsch potentials is constructed for ideal magnetohydrodynamics, multifluid plasmas, and elasticity.

TL;DR: In this article, the authors make a connection between invariant circles and the renormalisation operator, and show that the stability of a simple fixed point of renormalization corresponds to a linear twist map.

TL;DR: In this paper, the authors illustrate the following transition sequences; period doubling and the U-sequence, intermittency, the periodic-quasiperiodic-chaotic sequence, frequency locking, and an alternating periodic-chotic sequence.

TL;DR: In this article, the authors established bounds on the number of modes which determine the solutions of the Navier-Stokes equations in 2-dimensional Rayleigh-Benard convection.

TL;DR: In this paper, a simplified version of the experimentally determined Poincare map is proposed, and several features of the bifurcations of this map are described, including phase locking, period doubling and period chaotic dynamics at different values of the stimulation parameters.

TL;DR: In this paper, numerically the interactions of a kink and an antikink in a parametrically modified sine-Gordon model with potential V(φ) = (1 − r)2(1 − cosφ)/(1 + r2 + 2rcosφ).

TL;DR: In this paper, it was shown that the correlation properties of the quantum and corresponding classical motions are only similar for very short time intervals ts, and that the evolution of quantum system unlike the classical one is stable.

TL;DR: In this paper, a unified treatment of polynomial eigenvalue soliton equations associated with sl(2) eigen value problems is given, where a single family of commuting Hamiltonians on a subalgebra of the loop algebra of sl( 2) is given.

TL;DR: In this article, the interaction of autowave sources is experimentally studied in an active chemical medium with excitable kinetics, and three types of vortices are considered: 1) a spiral wave rotating in a simply-connected medium.

TL;DR: In this article, a 2-dimensional smooth orientable, but not compact space of constant negative curvature with the topology of a torus is investigated, which contains an open end, i.e., an exceptional point at infinite distance, through which a particle or a wave can enter or leave, as in the exponential horn of certain antennas or loudspeakers.

TL;DR: In this article, the authors studied the routes to chaos for a Rayleigh-Benard experiment in mercury, as a function of two parameters, the Rayleigh number (R ) and the Chandrasekhar number (Q ).

TL;DR: In this article, a hierarchy of symmetries for the Kadomtsev-Petviashvili equation is presented, which depend on the space and time variables explicitly.

TL;DR: In this paper, the motion of the wave front is characterized in terms of α, β and γ, and the effect of fast absorption (b  0, 0 < γ < 1) that causes extinction within a finite time, may break the evolving pulse into several sub-pulses and causes the expanding front to reverse its direction.

TL;DR: In this paper, a theory of integrable Hamiltonian systems in two dimensions is presented, which admits to integrability of the orbits for magnetic or Coriolis forces as well as for forces derivable from a potential.

TL;DR: In this article, the authors derived an asymptotic nonlinear equation which directly describes the dynamics of the onset and stabilization of cellular structure: ƒ τ + τ +▿ 4 + ǫ 4 +ǫ α = 0.