Journal ArticleDOI
Hyperbolicity of infinite-dimensional drift systems
Valentin Afraimovich,Yakov Pesin +1 more
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TLDR
In this paper, the stability of trajectories in infinite-dimensional systems with strongly hyperbolic properties has been studied and a special "drift" type of perturbation in which a system with number n interacts only with systems with previous numbers has been considered.Abstract:
The authors study the stability of trajectories in infinite-dimensional systems which are perturbations of infinite chains of independent finite-dimensional systems with strongly hyperbolic properties. They consider a special 'drift' type of perturbation in which a system with number n interacts only with systems with previous numbers. They reduce the problem of stability to a problem of small perturbations in a special space with an appropriate metric and construct the corresponding version of perturbation theory. Their main result is to show that the type of hyperbolicity can be radically changed when the parameters of the system grow.read more
Citations
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Geometric integrators for the nonlinear Schrödinger equation
TL;DR: In this paper, the authors discuss the performance of both symplectic and multisymplectic integrators for the nonlinear Schrodinger equation (NLS) and discuss the interrelations among various geometric features.
Journal ArticleDOI
Symplectic integrators for the Ablowitz–Ladik discrete nonlinear Schrödinger equation
TL;DR: In this paper, the authors derived higher order symplectic schemes for the Ablowitz-Ladik discrete nonlinear Schrodinger Eq. (IDNLS) using generating functions and compared them with standard Runge-Kutta algorithms with respect to accuracy and integration time.
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Travelling waves in lattice models of multi-dimensional and multi-component media. I: General hyperbolic properties
V Afraimovich,Yakov Pesin +1 more
TL;DR: In this paper, the stability of motion in the form of travelling waves in lattice models of unbounded multi-dimensional and multi-component media with a nonlinear prime term and small coupling depending on a finite number of space coordinates was studied.
Journal ArticleDOI
Multiscale analysis of defective multiple-Hopf bifurcations
TL;DR: In this paper, an adapted version of the multiple scale method is formulated to analyze 1:1 resonant multiple Hopf bifurcations of discrete autonomous dynamical systems, in which, for quasi-static variations of the parameters, an arbitrary number m of critical eigenvalues simultaneously cross the imaginary axis.
Journal ArticleDOI
Multi-symplectic methods for generalized Schrödinger equations
A. L. Islas,C. M. Schober +1 more
TL;DR: Three new multi-symplectic schemes for the one-dimensional nonlinear Schrodinger equation and the two-dimensional Gross-Pitaevskii equation are developed, which exactly preserve a discrete multi-Symplectic conservation law.
References
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Journal ArticleDOI
Families of invariant manifolds corresponding to nonzero characteristic exponents
TL;DR: A theorem on conditional stability for a family of mappings of class C1 +, satisfying a condition more general than Ljapunov regularity, was proved in this paper.
Journal ArticleDOI
Spacetime chaos in coupled map lattices
TL;DR: In this article, it was shown that the Z2 dynamical system generated by space translations and dynamics has a unique invariant mixing Gibbs measure with absolutely continuous finite-dimensional projections.
Journal ArticleDOI
Low-dimensional chaos in a hydrodynamic system
A. Brandstater,Jack Swift,Harry L. Swinney,A. Wolf,J. Doyne Farmer,Erica Jen,P. J. Crutchfield +6 more
TL;DR: In this article, the largest Lyapunov exponent and metric entropy of the Couette-Taylor flow data were used to show that motion is restricted to an attractor of dimension 5 for Reynolds numbers.
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Lyapunov analysis and information flow in coupled map lattices
Kunihiko Kaneko,Kunihiko Kaneko +1 more
TL;DR: In this paper, the co-moving mutual information flow is introduced, which shows the selective transmission of the information at some speed, and the spatial structures of the vectors are investigated.
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Noise-sustained structure, intermittency, and the Ginzburg-Landau equation
TL;DR: In this article, the time-dependent generalized Ginzburgland-landau equation is studied in the presence of low-level external noise and it is found that themicroscopic noise plays an important role in themacroscopic dynamics of the system, in which the random nature of the external noise plays a crucial role.
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