Jump to ContentJump to Main Navigation
Show Summary Details
More options …

Advanced Nonlinear Studies

Editor-in-Chief: Ahmad, Shair

IMPACT FACTOR 2018: 1.650

CiteScore 2018: 1.49

SCImago Journal Rank (SJR) 2018: 1.422
Source Normalized Impact per Paper (SNIP) 2018: 0.865

Mathematical Citation Quotient (MCQ) 2017: 1.03

See all formats and pricing
More options …
Volume 8, Issue 1


Dynamics of Generic Multidimensional Linear Differential Systems

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


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.

Export Citation

© 2016 by Advanced Nonlinear Studies, Inc..

Citing Articles

Here you can find all Crossref-listed publications in which this article is cited. If you would like to receive automatic email messages as soon as this article is cited in other publications, simply activate the “Citation Alert” on the top of this page.

Mário Bessa and Glória Ferreira Carvalho
Journal of Evolution Equations, 2019
Mário Bessa and Helder Vilarinho
Journal of Differential Equations, 2014, Volume 256, Number 7, Page 2337
Ergodic Theory and Dynamical Systems, 2013, Volume 33, Number 06, Page 1709
Nguyen Cong and Doan Thai Son
Discrete and Continuous Dynamical Systems - Series S, 2016, Volume 9, Number 4, Page 995
Mário Bessa and Jorge Rocha
Journal of Differential Equations, 2008, Volume 245, Number 11, Page 3127

Comments (0)

Please log in or register to comment.
Log in