Author:
ALVES LUCIANA A.,SAN MARTIN LUIZ A. B.
Abstract
Let$Q\rightarrow X$be a continuous principal bundle whose group$G$is reductive. A flow${\it\phi}$of automorphisms of$Q$endowed with an ergodic probability measure on the compact base space$X$induces two decompositions of the flag bundles associated to$Q$: a continuous one given by the finest Morse decomposition and a measurable one furnished by the multiplicative ergodic theorem. The second is contained in the first. In this paper we find necessary and sufficient conditions so that they coincide. The equality between the two decompositions implies continuity of the Lyapunov spectra under perturbations leaving unchanged the flow on the base space.
Publisher
Cambridge University Press (CUP)
Subject
Applied Mathematics,General Mathematics
Cited by
3 articles.
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1. On the global behavior of linear flows;Proceedings of the American Mathematical Society;2022-09-09
2. Lyapunov exponents and partial hyperbolicity of chain control sets on flag manifolds;Israel Journal of Mathematics;2019-07-09
3. Flag Type of Semigroups: A Survey;Advances in Mathematics and Applications;2018