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Korean Mathematical Society JKMS

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J. Korean Math. Soc. 1998; 35(2): 449-463

Printed June 1, 1998

Copyright © The Korean Mathematical Society.

Orbital Lipschitz stability and exponential asymptotic stability in dynamical systems

Jong-Myung Kim, Young-Hee Kye, and Keon-Hee Lee

Kwandong University, Kosin University and Chungnam National University

Abstract

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In this paper we introduce the notions of orbital Lipschitz stability (in variation) and orbital exponential asymptotic stability (in variation) of $C^r$ dynamical systems (or $C^r$ diffeomorphisms) on Riemannian manifolds, and study the embedding problem of those concepts in $C^r$ dynamical systems.

Keywords: embedding, dynamical systems, orbital Lipschitz stability, exponential asymptotic stability

MSC numbers: 58F, 54H

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