Hostname: page-component-cd9895bd7-jkksz Total loading time: 0 Render date: 2024-12-26T05:07:33.288Z Has data issue: false hasContentIssue false

Recurrence in Lipschitz stable flows

Published online by Cambridge University Press:  17 April 2009

Keon-Hee Lee
Affiliation:
Department of Mathematics, Chungnam National University, Daejeon, Korea (300–31)
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

The purpose of this paper is to get some necessary conditions for a Poisson stable flow to be recurrent and to analyse the bilateral versions of positive and negative Lipschitz stability. Moreover, a characterisation of recurrent orbits is obtained in a certain flow.

Type
Research Article
Copyright
Copyright © Australian Mathematical Society 1988

References

[1]Bhatia, N. and Hajek, O., Local semi-dynamical systems 90: Lecture Notes in Math. (Springer-Verlag, Berlin and New York, 1969).CrossRefGoogle Scholar
[2]Bhatia, N. and Szegö, G., Stability theory of dynamical systems (Springer-Verlag, Berlin and New York, 1970).CrossRefGoogle Scholar
[3]Elaydi, S. and Farran, H.R., ‘On weak isometrics and their embeddings in flows’, Nonlinear Analysis TMA 8 (1984), 14371441.CrossRefGoogle Scholar
[4]Elaydi, S. and Farran, H.R., ‘Isometrics and certain dynamical systems’, Bull. Austral. Math. Soc. 30 (1984), 239246.Google Scholar
[5]Elaydi, S. and Farran, H.R., ‘Lipschitz stable dynamical systems’, Nonlinear Anal. 9 (1985), 729738.CrossRefGoogle Scholar
[6]Knight, R., ‘Recurrent and Poisson stable flows’, Proc. Amer. Math. Soc. 83 (1981), 4953.Google Scholar
[7]Knight, R., ‘A characterisation of recurrent motions’, Bull. Austral. Math. Soc. 28 (1983), 14.CrossRefGoogle Scholar