Geodesic fields for Pontryagin type Co-Finsler manifolds = Campo geodésico para variedades de Finsler de classe Co do tipo Pontryagin

Abstract

In this work we define a class of C0-Finsler structures F on a differentiable manifold M which we call of Pontryagin type. In this type of structure it is possible to define a control system for the problem of minimizingthearclengthofacurveconnecting twopointsof (M;F) under the conditions of Pontryagin's maximum principle. It establishes necessary conditions for na admissible control and the respective solution to be optimal. As the Pontryagin's maximum principle is developed through the Hamiltonian formalism, we obtain Hamiltonian Fields from this process on the cotangent bundle of the manifold and When submitting such Fields to thecondition of the maximum principle, we obtain the extended geodesic field.