MULTIPLICATIVE ERGODIC THEOREM ON FLAG BUNDLES OF SEMI-SIMPLE LIE GROUPS

Autor(es)

Alves, Luciana A. ^[1] ; San Martin, Luiz A. B. ^[2]

Afiliação do(s) autor(es)

^[1] Univ Fed Uberlandia, Fac Matemat, BR-38408100 Uberlandia, MG - Brazil

^[2] Imecc Unicamp, Dept Matemat, Campinas, SP - Brazil

• Tipo de documento: Artigo Científico
• Fonte: DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS; v. 33, n. 4, p. 1247-1273, APR 2013.
• Citações Web of Science: 2

Resumo

Let Q -> X be a principal bundle having as structural group G a reductive Lie group in the Harish-Chandra class that includes the case when G is semi-simple with finite center. A semiflow phi(k) of endomorphisms of Q induces a semiflow psi(k) on the associated bundle E = Q x(G) F, where F is the maximal flag bundle of G. The A-component of the Iwasawa decomposition G = KAN yields an additive vector valued cocycle a (k, xi), xi is an element of E, over psi(k) with values in the Lie algebra a of A. We prove the Multiplicative Ergodic Theorem of Oseledets for this cocycle: If nu is a probability measure invariant by the semiflow on X then the a-Lyapunov exponent lambda (xi) = lim 1/ka (k, xi) exists for every xi on the fibers above a set of full nu-measure. The level sets of lambda (.) on the fibers are described in algebraic terms. When phi(k) is a flow the description of the level sets is sharpened. We relate the cocycle a (k, xi) with the Lyapunov exponents of a linear flow on a vector bundle and other growth rates. (AU)

• Processo FAPESP: 07/06896-5 - Geometria de sistemas de controle, sistemas dinâmicos e estocásticos
• Beneficiário: Luiz Antonio Barrera San Martin
• Modalidade de apoio: Auxílio à Pesquisa - Temático
• Processo FAPESP: 06/60031-3 - Fluxos em fibrados sobre espaços homogêneos
• Beneficiário: Luciana Aparecida Alves
• Modalidade de apoio: Bolsas no Brasil - Doutorado