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Morse and Lyapunov spectra and dynamics on flag bundles

Published online by Cambridge University Press:  23 June 2009

LUIZ A. B. SAN MARTIN  and
LUCAS SECO
LUIZ A. B. SAN MARTIN
Affiliation:
Instituto de Matemática, Universidade Estadual de Campinas, Cx. Postal 6065, 13.081-970 Campinas-SP, Brasil (email: [email protected])
LUCAS SECO
Affiliation:
Instituto de Matemática, Universidade Estadual de Campinas, Cx. Postal 6065, 13.081-970 Campinas-SP, Brasil (email: [email protected])
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Abstract

In this paper we study characteristic exponents of flows in relation with the dynamics of flows on flag bundles. The starting point is a flow on a principal bundle with semi-simple group G. Projection against the Iwasawa decomposition G=KAN defines an additive cocycle over the flow with values in 𝔞=log A. Its Lyapunov exponents (limits along trajectories) and Morse exponents (limits along chains) are studied. A symmetric property of these spectral sets is proved, namely invariance under the Weyl group. We also prove that these sets are located in certain Weyl chambers, defined from the dynamics on the associated flag bundles. As a special case linear flows on vector bundles are considered.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 30 , Issue 3 , June 2010 , pp. 893 - 922
Copyright
Copyright © Cambridge University Press 2009

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