Jordan decomposition and the recurrent set of flows of automorphisms

Víctor Ayala; Adriano da Silva; Philippe Jouan

doi:10.3934/dcds.2020330

Jordan decomposition and the recurrent set of flows of automorphisms

Víctor Ayala
, Adriano da Silva
, Philippe Jouan

Institute of Higher Research

Universidade Estadual de Campinas
Université de Rouen Normandie

Research output: Contribution to journal › Article › peer-review

5 Scopus citations

Abstract

In this paper we show that any linear vector field 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.

Original language	English
Pages (from-to)	1543-1559
Number of pages	17
Journal	Discrete and Continuous Dynamical Systems- Series A
Volume	41
Issue number	4
DOIs	https://doi.org/10.3934/dcds.2020330
State	Published - Apr 2021

Keywords

Jordan decomposition
Linear vector fields
Recurrent points

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10.3934/dcds.2020330

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title = "Jordan decomposition and the recurrent set of flows of automorphisms",

abstract = "In this paper we show that any linear vector field 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.",

keywords = "Jordan decomposition, Linear vector fields, Recurrent points",

author = "V{\'i}ctor Ayala and \{da Silva\}, Adriano and Philippe Jouan",

year = "2021",

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language = "English",

volume = "41",

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journal = "Discrete and Continuous Dynamical Systems- Series A",

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T1 - Jordan decomposition and the recurrent set of flows of automorphisms

AU - Ayala, Víctor

AU - da Silva, Adriano

AU - Jouan, Philippe

PY - 2021/4

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N2 - In this paper we show that any linear vector field 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.

AB - In this paper we show that any linear vector field 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.

KW - Jordan decomposition

KW - Linear vector fields

KW - Recurrent points

UR - https://www.scopus.com/pages/publications/85101110654

U2 - 10.3934/dcds.2020330

DO - 10.3934/dcds.2020330

M3 - Article

AN - SCOPUS:85101110654

SN - 1078-0947

VL - 41

SP - 1543

EP - 1559

JO - Discrete and Continuous Dynamical Systems- Series A

JF - Discrete and Continuous Dynamical Systems- Series A

IS - 4

ER -

Jordan decomposition and the recurrent set of flows of automorphisms

Abstract

Keywords

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