Control systems on flag manifolds and their chain control sets

Victor Ayala; Adriano Da Silva; Luiz A.B. San Martin

doi:10.3934/dcds.2017101

Control systems on flag manifolds and their chain control sets

Victor Ayala
, Adriano Da Silva
, Luiz A.B. San Martin

Institute of Higher Research

Universidad Católica del Norte
Universidade Estadual de Campinas

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

5 Scopus citations

Abstract

A right-invariant control system Σ on a connected Lie group G induce affine control systems Σo on every flag manifold Fe = G=Pe. In this paper we show that the chain control sets of the induced systems coincides with their analogous one defined via semigroup actions. Consequently, any chain control set of the system contains a control set with nonempty interior and, if the number of the control sets with nonempty interior coincides with the number of the chain control sets, then the closure of any control set with nonempty interior is a chain control set. Some relevant examples are included.

Original language	English
Pages (from-to)	2301-2313
Number of pages	13
Journal	Discrete and Continuous Dynamical Systems- Series A
Volume	37
Issue number	5
DOIs	https://doi.org/10.3934/dcds.2017101
State	Published - May 2017

Keywords

Chain control sets
Control systems
Flag manifolds
Semigroups

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10.3934/dcds.2017101

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title = "Control systems on flag manifolds and their chain control sets",

abstract = "A right-invariant control system Σ on a connected Lie group G induce affine control systems Σo on every flag manifold Fe = G=Pe. In this paper we show that the chain control sets of the induced systems coincides with their analogous one defined via semigroup actions. Consequently, any chain control set of the system contains a control set with nonempty interior and, if the number of the control sets with nonempty interior coincides with the number of the chain control sets, then the closure of any control set with nonempty interior is a chain control set. Some relevant examples are included.",

keywords = "Chain control sets, Control systems, Flag manifolds, Semigroups",

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N2 - A right-invariant control system Σ on a connected Lie group G induce affine control systems Σo on every flag manifold Fe = G=Pe. In this paper we show that the chain control sets of the induced systems coincides with their analogous one defined via semigroup actions. Consequently, any chain control set of the system contains a control set with nonempty interior and, if the number of the control sets with nonempty interior coincides with the number of the chain control sets, then the closure of any control set with nonempty interior is a chain control set. Some relevant examples are included.

AB - A right-invariant control system Σ on a connected Lie group G induce affine control systems Σo on every flag manifold Fe = G=Pe. In this paper we show that the chain control sets of the induced systems coincides with their analogous one defined via semigroup actions. Consequently, any chain control set of the system contains a control set with nonempty interior and, if the number of the control sets with nonempty interior coincides with the number of the chain control sets, then the closure of any control set with nonempty interior is a chain control set. Some relevant examples are included.

KW - Chain control sets

KW - Control systems

KW - Flag manifolds

KW - Semigroups

UR - https://www.scopus.com/pages/publications/85017541375

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DO - 10.3934/dcds.2017101

M3 - Article

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JO - Discrete and Continuous Dynamical Systems- Series A

JF - Discrete and Continuous Dynamical Systems- Series A

IS - 5

ER -

Control systems on flag manifolds and their chain control sets

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Keywords

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