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 [1] and the Morse and Lyapunov spectrum
of the control system can be recovered from the vectorial exponents introduced in [2].


[1] 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.

[2] 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.