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LOWER BOUNDS ALONG STABLE MANIFOLDS

Part of:Smooth dynamical systems: general theoryStability theory

Published online by Cambridge University Press:  02 October 2017

LUIS BARREIRA and
CLAUDIA VALLS
LUIS BARREIRA
Affiliation:
Departamento de Matemática, Instituto Superior Técnico, Universidade de Lisboa, 1049-001 Lisboa, Portugal e-mail: barreira@math.tecnico.ulisboa.pt, cvalls@math.tecnico.ulisboa.pt
CLAUDIA VALLS
Affiliation:
Departamento de Matemática, Instituto Superior Técnico, Universidade de Lisboa, 1049-001 Lisboa, Portugal e-mail: barreira@math.tecnico.ulisboa.pt, cvalls@math.tecnico.ulisboa.pt
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Abstract

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It is well known that along any stable manifold the dynamics travels with an exponential rate. Moreover, this rate is close to the slowest exponential rate along the stable direction of the linearization, provided that the nonlinear part is sufficiently small. In this note, we show that whenever there is also a fastest finite exponential rate along the stable direction of the linearization, similarly we can establish a lower bound for the speed of the nonlinear dynamics along the stable manifold. We consider both cases of discrete and continuous time, as well as a nonuniform exponential behaviour.

MSC classification

Primary:34D99: None of the above, but in this section
Secondary:37C75: Stability theory

Information

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 60 , Issue 3 , September 2018, pp. 527 - 537
Copyright
Copyright © Glasgow Mathematical Journal Trust 2017 

References

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