Chaos indicator and integrability conditions from geometrodynamics

Integrability and Chaos – algebraic and geometric approach

Nonlinear Physics: Integrability, Chaos and Beyond

Integrability and chaos are two of the main concepts associated with nonlinear physical systems which have revolutionized our understanding of them. Highly stable exponentially localized solitons are often associated with many of the important integrable nonlinear systems while motions which are sensitively dependent on initial conditions are associated with chaotic systems. Besides dramaticall...

~) Pergamon Nonlinear Physics." Integrability, Chaos and Beyond

In teyrability and chaos are two o f the main concepts associated with nonlinear physical systems which have revolutionized our understanding o f them. Highly stable exponentially localized solitons are often associated with many o f the important inteyrable nonlinear systems while motions which are sensitively dependent on initial conditions are associated with chaotic systems. Besides dramati...

On Integrability and Chaos in Discrete Systems

The scalar nonlinear Schrödinger (NLS) equation and a suitable discretization are well known integrable systems which exhibit the phenomena of “effective” chaos. Vector generalizations of both the continuous and discrete system are discussed. Some attention is directed upon the issue of the integrability of a discrete version of the vector NLS equation.

Lagrangian structures, integrability and chaos for 3D dynamical equations

In this paper we consider the general setting for constructing Action Principles for three–dimensional first order autonomous equations. We present the results for some integrable and non–integrable cases of the Lotka–Volterra equation, and we show Lagrangian descriptions which are valid for systems satisfying Shil’nikov criteria on the existence of strange attractors, though chaotic behavior o...