Geometry of optimal control problems and Hamiltonian systems

Details Geometry of optimal control problems and Hamiltonian systems Geometry of optimal control problems and Hamiltonian systems

2005-06-10

arxiv.org/abs/math/0506197v1

Mathematics

Optimization and Control

Lecture Notes

Scientific paper

These notes are based on the mini-course given in June 2004 in Cetraro, Italy, in the frame of a C.I.M.E. school. Of course, they contain much more material that I could present in the 6 hours course. The main goal is to give an idea of the general variational and dynamical nature of nice and powerful concepts and results mainly known in the narrow framework of Riemannian Geometry. This concerns Jacobi fields, Morse's index formula, Levi Civita connection, Riemannian curvature and related topics. I tried to make the presentation as light as possible: gave more details in smooth regular situations and referred to the literature in more complicated cases.

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