IJPAM: Volume 58, No. 2 (2010)

COMPLETE LYAPUNOV SURFACES

Efthimios Kappos
Department of Mathematics
School of General Sciences
Faculty of Engineering
University of Thessaloniki
Thessaloniki, 54124, GREECE
e-mail: [email protected]


Abstract.In this paper we prove the existence of transverse submanifolds intersecting each orbit in the region of attraction of a general attractor exactly once. We call these complete Lyapunov surfaces. We relate this novel way at looking at the familiar Lyapunov function theory to the geometric notion of transverse foliations. We examine in some detail how Lyapunov surfaces can be moved along the flow and give arguments as to why they are in a sense more fundamental than Lyapunov functions.

Received: December 15, 2009

AMS Subject Classification: 37B25, 93D30

Key Words and Phrases: dynamical systems, Lyapunov stability, Lyapunov functions, Conley index

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2010
Volume: 58
Issue: 2