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NON-UNIFORM TRICHOTOMIES AND ARBITRARY GROWTH RATES

Part of: Stability theory Smooth dynamical systems: general theory

Published online by Cambridge University Press:  03 April 2017

Luis Barreira  and
Claudia Valls
Luis Barreira
Affiliation:
Departamento de Matemática, Instituto Superior Técnico, Universidade de Lisboa, 1049-001 Lisboa, Portugal email barreira@math.tecnico.ulisboa.pt
Claudia Valls
Affiliation:
Departamento de Matemática, Instituto Superior Técnico, Universidade de Lisboa, 1049-001 Lisboa, Portugal email cvalls@math.tecnico.ulisboa.pt
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Abstract

For a non-autonomous dynamics defined by a sequence of matrices, we consider the notion of a non-uniform exponential trichotomy for an arbitrary growth rate (this means that there may exist contracting, expanding and neutral directions with an arbitrary fixed growth rate). The purpose of our work is two-fold: to use a regularity coefficient in order to show that these trichotomies occur naturally and to provide several alternative characterizations of those for which the non-uniform part is arbitrarily small. This includes characterizations in terms of the growth rate of volumes and of the Lyapunov exponents of the dynamics and its adjoint. We also obtain sharp lower and upper bounds for the regularity coefficient.

MSC classification

Primary: 34D08: Characteristic and Lyapunov exponents 37C75: Stability theory
Type
Research Article
Information
Mathematika , Volume 63 , Issue 2 , 2017 , pp. 518 - 537
Copyright
Copyright © University College London 2017 

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