Chaotic numerics : an International Workshop on the Approximation and Computation of Complicated Dynamical Behavior, July 12-16, 1993, Deakin University, Geelong, Australia
著者
書誌事項
Chaotic numerics : an International Workshop on the Approximation and Computation of Complicated Dynamical Behavior, July 12-16, 1993, Deakin University, Geelong, Australia
（Contemporary mathematics, 172）
American Mathematical Society, c1994
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注記
Includes bibliographical references
"Workshop ... with support from the Faculty of Science and Technology of Deakin University and the Australian Mathematical Society"--T.p. verso
内容説明・目次
内容説明
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.
目次
Numerical dynamics by J. K. Hale Error backward by R. M. Corless Modified equations for ODEs by M. P. Calvo, A. Murua, and J. M. Sanz-Serna The dynamics of some iterative implicit schemes by H. C. Yee and P. K. Sweby Shadowing of lattice maps by S.-N. Chow and E. S. Van Vleck Periodic shadowing by B. A. Coomes, H. Koccccccak, and K. J. Palmer On well-posed problems for connecting orbits in dynamical systems by W.-J. Beyn Numerical computation of a branch of invariant circles starting at a Hopf bifurcation point by L. Debraux Numerics of invariant manifolds and attractors by J. Lorenz Interval stochastic matrices and simulation of chaotic dynamics by P. Diamond, P. Kloeden, and A.Pokrovskii Mathematical and numerical analysis of a mean-field equation for the Ising model with Glauber dynamics by C. M. Elliott, A. R. Gardiner, I. Kostin, and B. Lu Attractors for weakly coupled map lattices by V. M. Gundlach Effective chaos in the nonlinear Schrodinger equation by M. J. Ablowitz and C. M. Schober Discretisation effect on a dynamical system with discontinuity by X. Yu.
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