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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| Format: | Electronic |
| Language: | English |
| Published: |
Providence :
American Mathematical Society,
1994.
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| Series: | Contemporary Mathematics Ser.
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| Subjects: | |
| Online Access: | Click for online access |
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| 035 | |a (OCoLC)1037814025 | ||
| 050 | 4 | |a QA614.8.I62 1993 | |
| 049 | |a HCDD | ||
| 100 | 1 | |a Kloeden, Peter E. | |
| 245 | 1 | 0 | |a Chaotic Numerics. |
| 260 | |a Providence : |b American Mathematical Society, |c 1994. | ||
| 300 | |a 1 online resource (290 pages) | ||
| 336 | |a text |b txt |2 rdacontent | ||
| 337 | |a computer |b c |2 rdamedia | ||
| 338 | |a online resource |b cr |2 rdacarrier | ||
| 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. | |
| 856 | 4 | 0 | |u https://holycross.idm.oclc.org/login?auth=cas&url=https://ebookcentral.proquest.com/lib/holycrosscollege-ebooks/detail.action?docID=5295210 |y Click for online access |
| 903 | |a EBC-AC | ||
| 994 | |a 92 |b HCD | ||