Jordan decomposition and the recurrent set of flows of automorphisms

@article{Ayala2021JordanDA,
  title={Jordan decomposition and the recurrent set of flows of automorphisms},
  author={V{\'i}ctor Ayala and Adriano Da Silva and Philippe Jouan},
  journal={Discrete \& Continuous Dynamical Systems - A},
  year={2021}
}
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 ow 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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