Fractional embeddings and stochastic time

Jacky Cresson (1, 2) , Pierre Inizan (1)

1 IMCCE - Institut de Mécanique Céleste et de Calcul des Ephémérides
2 LMAP - Laboratoire de Mathématiques et de leurs Applications [Pau]

As a model problem for the study of chaotic Hamiltonian systems, we look for the effects of a long-tail distribution of recurrence times on a fixed Hamiltonian dynamics. We follow Stanislavsky's approach of Hamiltonian formalism for fractional systems. We prove that his formalism can be retrieved from the fractional embedding theory. We deduce that the fractional Hamiltonian systems of Stanislavsky stem from a particular least action principle, said causal. In this case, the fractional embedding becomes coherent.

Mots clés: Lagrangian and Hamiltonian dynamics; fractional calculus; least action principle; stochastic processes

Domaines: Systèmes dynamiques [math.DS]; Physique mathématique [math-ph]

Jacky Cresson, Pierre Inizan. Fractional embeddings and stochastic time. 2008. ⟨hal-00324468⟩