# American Institute of Mathematical Sciences

doi: 10.3934/dcds.2020330

## 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

Received  February 2020 Revised  August 2020 Published  September 2020

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

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.

Citation: Víctor Ayala, Adriano Da Silva, Philippe Jouan. Jordan decomposition and the recurrent set of flows of automorphisms. Discrete & Continuous Dynamical Systems - A, doi: 10.3934/dcds.2020330
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