Chaotic Numerics

by Kloeden, Peter; Palmer, Kenneth J.

• ISBN13: 9780821851845
• ISBN10: 0821851845
• Format: Paperback
• Copyright: 1994-07-01
• Publisher: Amer Mathematical Society

Summary

Much of what is known about specific dynamical systems is obtained from numerical experiments. Although the discretization process usually has no significant effect on the results for simple, well-behaved dynamics, acute sensitivity to changes in initial conditions is a hallmark of chaotic behavior. How confident can one be that the numerical dynamics reflects that of the original system? Do numerically calculated trajectories always shadow a true one? What role does numerical analysis play in the study of dynamical systems? And conversely, can advances in dynamical systems provide new insights into numerical algorithms? These and related issues were the focus of the workshop on Chaotic Numerics, held at Deakin University in Geelong, Australia, in July 1993. The contributions to this book are based on lectures presented during the workshop and provide a broad overview of this area of research.

Table of Contents

Numerical dynamics

Error backward

Modified equations for ODEs

The dynamics of some iterative implicit schemes

Shadowing of lattice maps

Periodic shadowing

On well-posed problems for connecting orbits in dynamical systems

Numerical computation of a branch of invariant circles starting at a Hopf bifurcation point

Numerics of invariant manifolds and attractors

Interval stochastic matrices and simulation of chaotic dynamics

Mathematical and numerical analysis of a mean-field equation for the Ising model with Glauber dynamics

Attractors for weakly coupled map lattices

Effective chaos in the nonlinear Schrodinger equation

Discretisation effect on a dynamical system with discontinuity

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