Lyapunov exponents and partial hyperbolicity of chain control sets on flag manifolds

Adriano Da Silva; Christoph Kawan

doi:10.1007/s11856-019-1893-3

Lyapunov exponents and partial hyperbolicity of chain control sets on flag manifolds

Adriano Da Silva
, Christoph Kawan

Universidade Estadual de Campinas
Ludwig Maximilian University of Munich

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

4 Scopus citations

Abstract

For a right-invariant control system on a flag manifold F_Θ of a real semisimple Lie group, we relate the a-Lyapunov exponents to the Lyapunov exponents of the system over regular points. Moreover, we adapt the concept of partial hyperbolicity from the theory of smooth dynamical systems to control-affine systems, and we completely characterize the partially hyperbolic chain control sets on F_Θ.

Original language	English
Pages (from-to)	947-1000
Number of pages	54
Journal	Israel Journal of Mathematics
Volume	232
Issue number	2
DOIs	https://doi.org/10.1007/s11856-019-1893-3
State	Published - 1 Aug 2019
Externally published	Yes

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title = "Lyapunov exponents and partial hyperbolicity of chain control sets on flag manifolds",

abstract = "For a right-invariant control system on a flag manifold FΘ of a real semisimple Lie group, we relate the a-Lyapunov exponents to the Lyapunov exponents of the system over regular points. Moreover, we adapt the concept of partial hyperbolicity from the theory of smooth dynamical systems to control-affine systems, and we completely characterize the partially hyperbolic chain control sets on FΘ.",

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AU - Kawan, Christoph

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N2 - For a right-invariant control system on a flag manifold FΘ of a real semisimple Lie group, we relate the a-Lyapunov exponents to the Lyapunov exponents of the system over regular points. Moreover, we adapt the concept of partial hyperbolicity from the theory of smooth dynamical systems to control-affine systems, and we completely characterize the partially hyperbolic chain control sets on FΘ.

AB - For a right-invariant control system on a flag manifold FΘ of a real semisimple Lie group, we relate the a-Lyapunov exponents to the Lyapunov exponents of the system over regular points. Moreover, we adapt the concept of partial hyperbolicity from the theory of smooth dynamical systems to control-affine systems, and we completely characterize the partially hyperbolic chain control sets on FΘ.

UR - https://www.scopus.com/pages/publications/85068906126

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DO - 10.1007/s11856-019-1893-3

M3 - Article

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VL - 232

SP - 947

EP - 1000

JO - Israel Journal of Mathematics

JF - Israel Journal of Mathematics

IS - 2

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Lyapunov exponents and partial hyperbolicity of chain control sets on flag manifolds

Abstract

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