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Advanced Nonlinear Studies

Editor-in-Chief: Ahmad, Shair


IMPACT FACTOR 2018: 1.650

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Volume 8, Issue 1

Issues

Dynamics of Generic Multidimensional Linear Differential Systems

Mário Bessa
Published Online: 2016-03-10 | DOI: https://doi.org/10.1515/ans-2008-0107

Abstract

We prove that there exists a residual subset R (with respect to the C0 topology) of d-dimensional linear differential systems based in a μ-invariant flow and with transition matrix evolving in GL(d,ℝ) such that if A ∈ R, then, for μ-a.e. point, the Oseledets splitting along the orbit is dominated (uniform projective hyperbolicity) or else the Lyapunov spectrum is trivial. Moreover, in the conservative setting, we obtain the dichotomy: dominated splitting versus zero Lyapunov exponents.

Keywords: Linear Differential Systems; Dominated splitting; Lyapunov exponents; Multiplicative ergodic theorem

About the article

Published Online: 2016-03-10

Published in Print: 2008-02-01


Citation Information: Advanced Nonlinear Studies, Volume 8, Issue 1, Pages 191–211, ISSN (Online) 2169-0375, ISSN (Print) 1536-1365, DOI: https://doi.org/10.1515/ans-2008-0107.

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© 2016 by Advanced Nonlinear Studies, Inc..

Citing Articles

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[1]
LUCAS BACKES, MAURICIO POLETTI, PAULO VARANDAS, and YURI LIMA
Ergodic Theory and Dynamical Systems, 2019, Page 1
[2]
Mário Bessa and Glória Ferreira Carvalho
Journal of Evolution Equations, 2019
[3]
Mário Bessa and Helder Vilarinho
Journal of Differential Equations, 2014, Volume 256, Number 7, Page 2337
[4]
MÁRIO BESSA and JORGE ROCHA
Ergodic Theory and Dynamical Systems, 2013, Volume 33, Number 06, Page 1709
[5]
Nguyen Cong and Doan Thai Son
Discrete and Continuous Dynamical Systems - Series S, 2016, Volume 9, Number 4, Page 995
[6]
Mário Bessa and Jorge Rocha
Journal of Differential Equations, 2008, Volume 245, Number 11, Page 3127

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