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Chaotic Dynamics papers — page 69

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The Classical and Quantum Mechanics of Lazy Baker Maps
We introduce and study the classical and quantum mechanics of certain non hyperbolic maps on the unit square. These maps are modifications of the usual baker's map and their behaviour ranges from…
A. Lakshminarayan, N. L. BalazsJul 12, 1993
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Relaxation and Localization in Interacting Quantum Maps
We quantise and study several versions of finite multibaker maps. Classically these are exactly solvable K-systems with known exponential decay to global equilibrium. This is an attempt to construct…
A. Lakshminarayan, N. L. BalazsJul 11, 1993
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Scale resolved intermittency in turbulence
The deviations δζm ("intermittency corrections") from classical ("K41") scaling ζm=m/3 of the mth moments of the velocity differences in high Reynolds number turbulence are…
Siegfried Grossmann, Detlef LohseJul 9, 1993
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Dynamical zeta functions for Artin's billiard and the Venkov--Zograf factorization formula
Dynamical zeta functions are expected to relate the Schrödinger operator's spectrum to the periodic orbits of the corresponding fully chaotic Hamiltonian system. The relationsship is exact in the…
Michael Eisele, Dieter MayerJul 2, 1993
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Stable Non-Gaussian Diffusive Profiles
We prove two stability results for the scale invariant solutions of the nonlinear heat equation ∂t u=Δu - |u|p-1u with 1<p<1+2 n, n being the spatial dimension. The first…
J. Bricmont, A. KupiainenJun 28, 1993
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Self-Preservation of Large-Scale Structures in Burgers' Turbulence
We investigate the stability of large-scale structures in Burgers' equation under the perturbation of high wave-number noise in the initial conditions. Analytical estimates are obtained for…
Erik Aurell, Sergey N. Gurbatov, Igor I. WertgeimJun 26, 1993
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Using Horseshoes to Create Coherent Structures
In this letter, we show that coherent structures are related to folds of horseshoes which are present in chaotic systems. We develop techniques that allow us to construct coherent structures by…
Troy Shinbrot, J. M. OttinoJun 24, 1993
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Stability of Moving Fronts in the Ginzburg-Landau Equation
We use Renormalization Group ideas to study stability of moving fronts in the Ginzburg-Landau equation in one spatial dimension. In particular, we prove stability of the real fronts under complex…
J. Bricmont, A. KupiainenJun 21, 1993
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Renormalization Group and Asymptotics of Solutions of Nonlinear Parabolic Equations
We present a general method for studying long time asymptotics of nonlinear parabolic partial differential equations. The method does not rely on a priori estimates such as the maximum principle. It…
J. Bricmont, A. Kupiainen, G. LinJun 21, 1993
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Universality in Blow-Up for Nonlinear Heat Equations
We consider the classical problem of the blowing-up of solutions of the nonlinear heat equation. We show that there exist infinitely many profiles around the blow-up point, and for each integer k,…
J. Bricmont, A. KupiainenJun 21, 1993
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Interaction of surface waves with vorticity in shallow water
Vortical flows in shallow water interact with long surface waves by virtue of the nonlinear terms of the fluid equations. Analytical formulae are derived that quantify the spontaneous generation of…
Enrique cerda, Fernando LundJun 18, 1993
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Stochastic chaos: An analog of quantum chaos
Some intriging connections between the properties of nonlinear noise driven systems and the nonlinear dynamics of a particular set of Hamilton's equation are discussed. A large class of…
Mark M. MillonasJun 10, 1993
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Synchronization of coupled maps and stable, dissipative windows
Synchronization among globally coupled, chaotic map lattices can be related to stable periodic windows in isolated chaotic maps. This relation provides a simple predictive tool for the understanding…
Troy ShinbrotJun 9, 1993
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Twistless KAM tori
A selfcontained proof of the KAM theorem in the Thirring model is discussed.
Giovanni GallavottiJun 9, 1993
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Exhibiting Randomness in Arithmetic using Mathematica and C
In my book "Algorithmic Information Theory" I explain how I constructed a million-character equation that proves that there is randomness in arithmetic. My book only includes a few pages from…
G J ChaitinJun 8, 1993
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Chaotic System on the Super Riemann Surface
A chaotic system of a nonrelativistic superparticle moving freely on the super Riemann surface (SRS) of genus g ≥ 2 is reviewed.
Shuji MATSUMOTO, Shozo UEHARA, Yukinori YASUIJun 4, 1993
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Threshold Analysis for the Inverse ac Josephson Effect
The inverse ac Josephson effect involves rf-induced (Shapiro) steps that cross over the zero-current axis; the phenomenon is of interest in voltage standard applications. The standard analysis of the…
G. Filatrella, B. A. Malomed, R. D. ParmentierMay 28, 1993
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The Effect of Focusing and Caustics on Exit Phenomena in Systems Lacking Detailed Balance
We study the trajectories followed by a particle subjected to weak noise when escaping from the domain of attraction of a stable fixed point. If detailed balance is absent, a focus may occur along…
Robert S. Maier, Daniel L. SteinMay 28, 1993
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Large Fluctuations in Stochastically Perturbed Nonlinear Systems: Applications in Computing
This is the transcript of a talk given at the 1992 Complex Systems Summer School. The theory of large fluctuations of stochastically perturbed continuous-time dynamical systems is reviewed, and the…
Robert S. MaierMay 28, 1993
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Formal Languages in Dynamical Systems
We treat here the interrelation between formal languages and those dynamical systems that can be described by cellular automata (CA). There is a well-known injective map which identifies any…
G. TrollMay 21, 1993
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Periodic Solutions of a System of Coupled Oscillators Near Resonance
Summary: A system of autonomous ordinary differential equations depending on a small parameter is considered such that the unperturbed system has an invariant manifold of periodic solutions that is…
Carmen ChiconeMay 17, 1993
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Some Studies on Arithmetical Chaos in Classical and Quantum Mechanics
Several aspects of classical and quantum mechanics applied to a class of strongly chaotic systems are studied. These consist of single particles moving without external forces on surfaces of constant…
Jens BolteMay 14, 1993
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The cost of compressible dynamics, time-reversibility, Maxwell's demon, and the second law
A tantalizing version of Maxwell's demon is presented which appears to operate reversibly. A container of hard core disks is separated into two chambers of equal volume by a membrane that selects…
P. A. SkordosMay 14, 1993
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Poincaré maps of Duffing--type oscillators and their reduction to circle maps. I. Analytic results
Bifurcation diagrams and plots of Lyapunov exponents in the r--Ω --plane for Duffing--type oscillators x +2r x +V'(x,Ωt) =0 exhibit a regular pattern of repeating selfsimilar…
G. Eilenberger, K. SchmidtMay 13, 1993
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A Semiclassical Calculation of Scars for a Smooth Potential
Bogomolny's formula for energy-smoothed scars is applied for the first time to a non-specific, non-scalable Hamiltonian, a 2-D anharmonic oscillator. The semiclassical theory reproduces well the…
Daniel Provost, Michel BarangerMay 7, 1993
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