DYNAMICS OF NUMERICAL APPROXIMATIONS

Authors
HALE JK
Citation
Jk. Hale, DYNAMICS OF NUMERICAL APPROXIMATIONS, Applied mathematics and computation, 89(1-3), 1998, pp. 5-15
Citations number
17
Categorie Soggetti
Mathematics,Mathematics
Journal title
Applied mathematics and computation → ACNP
ISSN journal
00963003
Volume
89
Issue
1-3
Year of publication
1998
Pages
5 - 15
Database
ISI
SICI code
0096-3003(1998)89:1-3<5:DONA>2.0.ZU;2-A
Abstract
Assuming that a differential equation has a hyperbolic invariant set, we discuss the existence of a similar invariant set for the map define d by a numerical approximation, as well as the closeness of these sets in the C-1-topology. Particular emphasis is given to equilibrium poin ts, periodic orbits and invariant tori for the differential equation. We present also a result on the preservation of structural stability f or gradient systems. (C) Elsevier Science Inc., 1998.