Symmetries and integrals of motion in optimal control

H. Sussmann

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Horizontal systems of rays arise in the study of integral curves of Hamiltonian systems $v_{H}$ on T*X, which are tangent to a given distribution V of hyperplanes on X. We investigate the local properties of systems of rays for general pairs (H,V) as well as for Hamiltonians H such that the corresponding Hamiltonian vector fields $v_{H}$ are horizontal with respect to V. As an example we explicitly calculate the space of horizontal geodesics and the corresponding systems of rays for the canonical...