Contemporary Mathematics 1994; 278 pp; softcover Volume: 172 Reprint/Revision History: reprinted 1999 ISBN10: 0821851845 ISBN13: 9780821851845 List Price: US$45 Member Price: US$36 Order Code: CONM/172
 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, wellbehaved 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. Readership Research mathematicians. Table of Contents  J. K. Hale  Numerical dynamics
 R. M. Corless  Error backward
 M. P. Calvo, A. Murua, and J. M. SanzSerna  Modified equations for ODEs
 H. C. Yee and P. K. Sweby  The dynamics of some iterative implicit schemes
 S.N. Chow and E. S. Van Vleck  Shadowing of lattice maps
 B. A. Coomes, H. Koçcccccak, and K. J. Palmer  Periodic shadowing
 W.J. Beyn  On wellposed problems for connecting orbits in dynamical systems
 L. Debraux  Numerical computation of a branch of invariant circles starting at a Hopf bifurcation point
 J. Lorenz  Numerics of invariant manifolds and attractors
 P. Diamond, P. Kloeden, and A. Pokrovskii  Interval stochastic matrices and simulation of chaotic dynamics
 C. M. Elliott, A. R. Gardiner, I. Kostin, and B. Lu  Mathematical and numerical analysis of a meanfield equation for the Ising model with Glauber dynamics
 V. M. Gundlach  Attractors for weakly coupled map lattices
 M. J. Ablowitz and C. M. Schober  Effective chaos in the nonlinear Schrödinger equation
 X. Yu  Discretisation effect on a dynamical system with discontinuity
