16 Result(s)
within
Chapter
Tassos Bountis
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Chapter and Conference Paper
Dynamics and Statistics of Weak Chaos in a 4-D Symplectic Map
The important phenomenon of “stickiness” of chaotic orbits in low dimensional dynamical systems has been investigated for several decades, in view of its applications to various areas of physics, such as class...
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Chapter
Hamiltonian Systems of Few Degrees of Freedom
In Chap. 2 we provide first an elementary introduction to some simple examples of Hamiltonian systems of one and two degrees of freedom. We describe the essential features of phase space plots and focus on the...
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Chapter
Normal Modes, Symmetries and Stability
The present Chapter studies nonlinear normal modes (NNMs) of coupled oscillators from an altogether different perspective. Focusing entirely on periodic boundary conditions and using the Fermi Pasta Ulam β (FP...
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Chapter
FPU Recurrences and the Transition from Weak to Strong Chaos
The present Chapter starts with a historical introduction to the FPU one-dimensional lattice as it was first integrated numerically by Fermi Pasta and Ulam in the 1950s and describes the famous paradox of the ...
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Chapter
The Statistical Mechanics of Quasi-stationary States
This Chapter adopts an altogether different approach to the study of chaos in Hamiltonian systems. We consider, in particular, probability distribution functions (pdfs) of sums of chaotic orbit variables in di...
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Chapter
Introduction
Chapter 1 starts by defining a dynamical system in terms of ordinary differential equations and presents the fundamental framework within which one can study the stability of their equilibrium (or fixed) point...
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Chapter
Local and Global Stability of Motion
In this Chapter, we discuss in a unified way equilibrium points, periodic orbits and their stability, which constitute local concepts of Hamiltonian dynamics together with ordered and chaotic motion, which are th...
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Chapter
Efficient Indicators of Ordered and Chaotic Motion
This Chapter opens with an introduction to the variational equations, derived by the linearization of the ordinary differential equations of a Hamiltonian system, and the equations of the tangent map, obtained by...
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Chapter
Localization and Diffusion in Nonlinear One-Dimensional Lattices
In this Chapter we focus on localization properties of nonlinear lattices in the configuration space of their spatial coordinates. In particular, we begin by discussing the phenomenon of exponentially localize...
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Chapter
Conclusions, Open Problems and Future Outlook
The final Chapter first summarizes and discusses the main conclusions described in the book. We then list a number of open problems, which we feel should be further pursued in continuation of what we have pres...
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Chapter and Conference Paper
Model Reduction of a Higher-Order KdV Equation for Shallow Water Waves
We present novel results on a non-integrable generalized KdV equation proposed by Fokas [A.S. Fokas, Physica D87, 145 (1995)], aiming to describe unidirectional solitary water waves with greater accuracy than ...
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Chapter
Discrete Breathers in Nonlinear Lattices: A Review and Recent Results
Localization phenomena in systems of many (often infinite) degrees of freedom have attracted attention in solid state physics, nonlinear optics, superconductivity and quantum mechanics. The type of localizatio...
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Chapter
Inductively Coupled Long Josephson Junctions: Collective Coordinate Analysis and I–V Characteristics
The collective coordinate analysis of soliton dynamics developed by McLaughlin and Scott for perturbed sine-Gordon equations is applied here to two inductively coupled Long Josephson Junctions (LJJ’s). It is foun...
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Chapter and Conference Paper
Fluxon trap** by inhomogeneities in long Josephson junctions
Following the approach of collective coordinates for the location X(t), and speed U(t), of a fluxon travelling in a long Josephson junction (LJJ), we show that the conditions of fluxon trap** by an array of ...
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Chapter and Conference Paper
On the analytic structure of chaos in dynamical systems
A number of new and exciting results on the chaotic properties of dynamical systems have been recently obtained by studying their movable singularities in the complex time plane. New, integrable systems were i...
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Chapter and Conference Paper
Periodic solutions of arbitrary period, variational methods
We have constructed by a rapidly convergent variational method the periodic solutions, analytic in the time t and with “arbitrary” (long) period, of the well known Hénon-Heiles System, described by the Hamiltonia...
