ISSN:
0945-3245
Keywords:
Mathematics Subject Classification (1991): 65L05, 58F09, 65J15
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
Notes:
Summary. On compact $m$ -dimensional discs, Morse-Smale differential systems having no periodic orbits are considered. The main result is that they are correctly reproduced by one-step discretization methods. For methods of order $p$ and stepsize $h$ sufficiently small, the time- $h$ -map of the induced local flow and the $h$ -discretized system are joined by a conjugacy $O(h^p)$ -near to the identity. The paper fits well in the rapidly growing list of results stating that hyperbolic/transversal structures are preserved by discretization. The proof relies heavily on techniques elaborated by Robbin (1971) in establishing his structural stability theorem on self-diffeomorphisms of compact $C^{\infty}$ manifolds.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/s002110050177
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