Jordan decomposition and the recurrent set of flows of automorphisms

Víctor Ayala; Adriano Da Silva; Philippe Jouan

doi:10.3934/dcds.2020330

Article Contents

2021, Volume 41, Issue 4: 1543-1559. Doi: 10.3934/dcds.2020330

This issue Previous Article Averaging of Hamilton-Jacobi equations along divergence-free vector fields Next Article A Liouville theorem of parabolic Monge-AmpÈre equations in half-space

Jordan decomposition and the recurrent set of flows of automorphisms

1.
Instituto de Alta Investigación, Universidad de Tarapacá, Arica, Chile
2.
Instituto de Matemática, Universidade Estadual de Campinas, Brazil
3.
Laboratoire de Mathématiques Raphaël Salem, Université de Rouen, France

^* Corresponding author: Víctor Ayala
^* Corresponding author: Víctor Ayala

Received: January 31, 2020

Revised: July 31, 2020

Early access: September 2020

Published: April 2021

Supported by Proyecto Fondecyt n° 1190142. Conicyt, Chile.
Supported by Fapesp grant n° 2018/10696-6

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Abstract

In this paper we show that any linear vector field $ \mathcal{X} $ on a connected Lie group $ G $ admits a Jordan decomposition and the recurrent set of the associated flow of automorphisms is given as the intersection of the fixed points of the hyperbolic and nilpotent components of its Jordan decomposition.

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Mathematics Subject Classification: 37B20, 54H20, 37B99.

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References

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