Jordan decomposition and dynamics  on flag manifolds

Thiago Ferraiol; Mauro Patrão; Lucas Seco

doi:10.3934/dcds.2010.26.923

Article Contents

2010, Volume 26, Issue 3: 923-947. Doi: 10.3934/dcds.2010.26.923

This issue Previous Article Boundary stabilization of the wave and Schrödinger equations in exterior domains Next Article Baire category and extremely non-normal points of invariant sets of IFS's

Jordan decomposition and dynamics on flag manifolds

1.
Departamento de Matemática, Universidade Estadual de Campinas, Cx. Postal 6065, Campinas-SP, 13.083-859
2.
Departamento de Matemática, Universidade de Brasília, Campus Darcy Ribeiro, Cx. Postal 4481, Brasília-DF, 70.904-970

Received: December 31, 2008

Revised: September 30, 2009

Published: August 2010

Abstract Related Papers Cited by

Abstract

Let $\g$ be a real semisimple Lie algebra and $G = \Int(\g)$. In this article, we relate the Jordan decomposition of $X \in \g$ (or $g \in G$) with the dynamics induced on generalized flag manifolds by the right invariant continuous-time flow generated by $X$ (or the discrete-time flow generated by $g$). We characterize the recurrent set and the finest Morse decomposition (including its stable sets) of these flows and show that its entropy always vanishes. We characterize the structurally stable ones and compute the Conley index of the attractor Morse component. When the nilpotent part of $X$ is trivial, we compute the Conley indexes of all Morse components. Finally, we consider the dynamical aspects of linear differential equations with periodic coefficients in $\g$, which can be regarded as an extension of the dynamics generated by an element $X \in \g$. In this context, we generalize Floquet theory and extend our previous results to this case.

Keywords:

Mathematics Subject Classification: Primary: 37B35, 22E46, 37C20; Secondary: 37B30, 37B40.

Citation:

Article Metrics

HTML views() PDF downloads(137) Cited by(0)

Jordan decomposition and dynamics on flag manifolds

Abstract

Access History

Article Metrics

Access History

Other Articles By Authors

Catalog

Jordan decomposition and dynamics on flag manifolds

Abstract

Access History

SHARE

Article Metrics

Access History

Other Articles By Authors

Catalog

Export File

Citation

Format

Content