The 1st part (D.Barilari) is introductory to the subject and covers some fundamental results.
The 2nd part (A.Agrachev) is more advanced, focused on abnormal extremals.
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From Davide Barilari
39 plays 0Goh and Generalized Legendre conditions. -
From Davide Barilari
23 plays 0Rigidity and abnormal curves. Some second order conditions -
From Davide Barilari
16 plays 0Abnormals in dimension three -
From Davide Barilari
32 plays 0Rank 2 distribution. Engel and Cartan distributions -
From Davide Barilari
16 plays 0Characteristic variety, continuation. Genericity conditions. -
From Davide Barilari
26 plays 0Symplectic characterization of abnormal extremals. Characteristic variety. -
From Davide Barilari
30 plays 0Examples. Isoperimetric problems. Symplectic geometry. -
From Davide Barilari
50 plays 0Evaluation map, end-point map and abnormal extremals. -
From Davide Barilari
38 plays 0Normal length-minimizers. The Heisenberg group, continuation. -
From Davide Barilari
50 plays 0Hamiltonian formulation. Abnormal length-minimizers in dimension three. -
From Davide Barilari
56 plays 0First-order conditions. Normal and abnormal length-minimizers. -
From Davide Barilari
75 plays 0Existence of length-minimizers. The Heisenberg group . Length vs Energy -
From Davide Barilari
77 plays 0Sub-Riemannian structures and Rashevski-Chow theorem -
From Davide Barilari
92 plays 0Vector fields, Lie brackets, Frobenius theorem -
From Davide Barilari
250 plays 0Introduction: Parking a car, rolling a ball