Control Systems on flag manifolds
Adriano Da Silva
Department of Mathematics
University of Campinas
Campinas – Brazil
In this talk we show how the geometric structures of a semisimple Lie group G influentiates
the behavioural properties of any control system on the flag manifolds of G induced by invariant
systems. In particular, control and chain control sets can be recover from the Morse sets
associated with the control flow using the theory in  and the Morse and Lyapunov spectrum
of the control system can be recovered from the vectorial exponents introduced in .
 Braga Barros, C.J and L.A.B. San Martin, Chain transitive sets for flows on flag bundles,
Forum Math., 19 (2007) pp. 19-60.
 San Martin, L.A.B. and L. Seco, Morse and Lyapunov spectra and dynamics on flag bun-
dles, Ergod. Th. & Dynam. Sys., 30 (2010), pp. 893 – 922.