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Pointwise convergence of gradient-like systems

✍ Scribed by Christian Lageman

Publisher
John Wiley and Sons
Year
2007
Tongue
English
Weight
232 KB
Volume
280
Category
Article
ISSN
0025-584X

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✦ Synopsis

Abstract

S. Łojasiewicz has shown that the ω ‐limit sets of the trajectories of analytic gradient systems consist of at most one point. We extend this result to the larger class of gradient‐like vector fields satisfying an angle condition. In particular, this includes gradient systems, defined by arbitrary C^1^ functions from an analytic‐geometric category. Corresponding pointwise convergence results are shown for discrete gradient‐like algorithms on a Riemannian manifold. This generalizes recent results by Absil, Mahony, and Andrews to the Riemannian geometry setting. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

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