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The structure of the bounded trajectories set of a scalar convex differential equation

Published online by Cambridge University Press:  12 July 2007

A. I. Alonso  and
R. Obaya
A. I. Alonso
Affiliation:
ETSII Departamento de Matemática Aplicada a la Ingeniería, Paseo del Cauce s/n. 47011, Universidad de Valladolid, Spainanaalo@wmatem.eis.uva.es
R. Obaya
Affiliation:
ETSII Departamento de Matemática Aplicada a la Ingeniería, Paseo del Cauce s/n. 47011, Universidad de Valladolid, Spainrafoba@wmatem.eis.uva.es
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Abstract

The present paper describes the topological and ergodic structure of the set of bounded trajectories of the flow defined by a scalar convex differential equation. We characterize the minimal subsets, the ergodic measures concentrated on them, and study the longtime behaviour of the bounded trajectories in terms of the Lyapunov exponents of the linearized equations. In particular, we obtain conditions that guarantee the existence of almost-periodic, almost-automorphic and recurrent solutions.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 133 , Issue 2 , April 2003 , pp. 237 - 263
Copyright
Copyright © Royal Society of Edinburgh 2003

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