The Pontryagin derivative in optimal control (Q600714)

Honouring Pontryagin's memory Gamkrelidze discusses in this interesting paper the Hamiltonian format of Pontryagin's maximum principle. After historical remarks he compares in the first section of his paper the principle with the Euler-Lagrange method and shows -- using Legrendre transformation and regular problems -- that the extremals in the Euler-Lagrange method can be represented as a Hamilton flow and how on the contrary the family of extremals is handled in the maximum principle. In the second section leaning on the master Hamiltonian and the corresponding vector field he discusses the Hamiltonian format of the maximum principle (in invariant formulation) using Lie derivative, duality with help of conjugation and differential-geometric invariants and makes a proposal in relation to the title of the paper.