Chaotic Numerics.

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....

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Bibliographic Details
Main Author: Kloeden, Peter E.
Other Authors: Palmer, Kenneth J.
Format: Electronic
Language:English
Published: Providence : American Mathematical Society, 1994.
Series:Contemporary Mathematics Ser.
Subjects:
Online Access:Click for online access
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245 1 0 |a Chaotic Numerics. 
260 |a Providence :  |b American Mathematical Society,  |c 1994. 
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490 1 |a Contemporary Mathematics Ser. ;  |v v. 172 
588 0 |a Print version record. 
505 0 |a Intro; Table of Contents; Preface; 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. 
505 8 |a Attractors for Weakly Coupled Map LatticesEffective Chaos in the Nonlinear SchrÃœdinger Equation; Discretisation Effect on a Dynamical System with Discontinuity. 
520 |a 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 insight. 
650 0 |a Differentiable dynamical systems  |v Congresses. 
650 0 |a Numerical analysis  |v Congresses. 
650 0 |a Chaotic behavior in systems  |v Congresses. 
650 7 |a Chaotic behavior in systems.  |2 fast  |0 (OCoLC)fst00852171 
650 7 |a Differentiable dynamical systems.  |2 fast  |0 (OCoLC)fst00893426 
650 7 |a Numerical analysis.  |2 fast  |0 (OCoLC)fst01041273 
655 7 |a Conference papers and proceedings.  |2 fast  |0 (OCoLC)fst01423772 
700 1 |a Palmer, Kenneth J. 
776 0 8 |i Print version:  |a Kloeden, Peter E.  |t Chaotic Numerics.  |d Providence : American Mathematical Society, ©1994  |z 9780821851845 
830 0 |a Contemporary Mathematics Ser. 
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