Nonlinear Iwasawa decomposition of control flows

Fritz Colonius; Paulo Régis C. Ruffino

doi:10.3934/dcds.2007.18.339

Article Contents

2007, Volume 18, Issue 2&3: 339-354. Doi: 10.3934/dcds.2007.18.339

This issue Previous Article Qualitative behavior of a class of stochastic parabolic PDEs with dynamical boundary conditions Next Article Necessary condition for the basin of attraction of a periodic orbit in non-smooth periodic systems

Nonlinear Iwasawa decomposition of control flows

Fritz Colonius^1, and
Paulo Régis C. Ruffino^2,

1.
Institut für Mathematik, Universität Augsburg, 86135 Augsburg
2.
Departamento de Matemática, Universidade Estadual de Campinas, 13.081-970 - Campinas - SP

Received: November 30, 2005

Revised: May 31, 2006

Published: May 2007

Abstract Related Papers Cited by

Abstract

Let $\varphi(t,\cdot,u)$ be the flow of a control system on a Riemannian manifold $M$ of constant curvature. For a given initial orthonormal frame $k$ in the tangent space $T_{x_{0}}M$ for some $x_{0}\in M$, there exists a unique decomposition $\varphi_{t}=\Theta_{t}\circ\rho_{t}$ where $\Theta_{t}$ is a control flow in the group of isometries of $M$ and the remainder component $\rho_{t}$ fixes $x_{0}$ with derivative $D\rho_{t}(k)=k\cdot s_{t}$ where $s_{t}$ are upper triangular matrices. Moreover, if $M$ is flat, an affine component can be extracted from the remainder.

Keywords:

Mathematics Subject Classification: Primary: 37J40.

Citation:

Article Metrics

HTML views() PDF downloads(115) Cited by(0)

Nonlinear Iwasawa decomposition of control flows

Abstract

Access History

Article Metrics

Access History

Other Articles By Authors

Catalog

Nonlinear Iwasawa decomposition of control flows

Abstract

Access History

SHARE

Article Metrics

Access History

Other Articles By Authors

Catalog

Export File

Citation

Format

Content