Displaying similar documents to “Lyapunov exponents for stochastic differential equations on semi-simple Lie groups”

An estimation of the controllability time for single-input systems on compact Lie Groups

Andrei Agrachev, Thomas Chambrion (2006)

ESAIM: Control, Optimisation and Calculus of Variations

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Geometric control theory and Riemannian techniques are used to describe the reachable set at time of left invariant single-input control systems on semi-simple compact Lie groups and to estimate the minimal time needed to reach any point from identity. This method provides an effective way to give an upper and a lower bound for the minimal time needed to transfer a controlled quantum system with a drift from a given initial position to a given final position. The bounds include...

Superposition rules and stochastic Lie–Scheffers systems

Joan-Andreu Lázaro-Camí, Juan-Pablo Ortega (2009)

Annales de l'I.H.P. Probabilités et statistiques

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This paper proves a version for stochastic differential equations of the Lie–Scheffers theorem. This result characterizes the existence of nonlinear superposition rules for the general solution of those equations in terms of the involution properties of the distribution generated by the vector fields that define it. When stated in the particular case of standard deterministic systems, our main theorem improves various aspects of the classical Lie–Scheffers result. We show that the stochastic...

Control systems on semi-simple Lie groups and their homogeneous spaces

Velimir Jurdjevic, Ivan Kupka (1981)

Annales de l'institut Fourier

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In the present paper, we consider the class of control systems which are induced by the action of a semi-simple Lie group on a manifold, and we give a sufficient condition which insures that such a system can be steered from any initial state to any final state by an admissible control. The class of systems considered contains, in particular, essentially all the bilinear systems. Our condition is semi-algebraic but unlike the celebrated Kalman criterion for linear systems, it is not...