| Author(s): |
San Martin, Luiz A. B.
[1]
Total Authors: 1
|
| Affiliation: | [1] Univ Estadual Campinas, Inst Math, Campinas, SP - Brazil
Total Affiliations: 1
|
| Document type: | Journal article |
| Source: | JOURNAL OF LIE THEORY; v. 30, n. 2, p. 587-616, 2020. |
| Web of Science Citations: | 0 |
| Abstract | |
Let G be a noncompact semi-simple Lie group with finite center and mu a probability measure on G. We consider (i) the semigroup S-mu, generated by the support of mu (with the assumption that intS(mu) not equal empty set); (ii) The spectral radii r(lambda) of the operators U-lambda (mu) where U-lambda is a (nonunitary) representation of G induced by a real character and (iii) the moment Lyapunov exponents gamma (lambda, x) of the i.i.d. random product on G defined by mu. The equality r(lambda) = gamma (lambda, x) holds in many cases. We give a necessary and sufficient condition to have S-mu = G in terms of the analyticity of the map lambda bar right arrow r(lambda). The condition is applied to measures obtained by solutions of invariant stochastic differential equations on G yielding a necessary and sufficient condition for the controllability of invariant control systems on G in terms of the largest eigenvalues of second order differential operators. (AU) | |