2008/09/25 by Jacky Cresson, Cresson, Jacky, Pierre Inizan +1
Mathematics · Physics and Astronomy · #Dynamical Systems (math.DS) #FOS: Mathematics #FOS: Physical sciences #Fractional Differential Equations Solutions #Iterative Methods for Nonlinear Equations #Mathematical Physics (math-ph) #Nonlinear Differential Equations Analysis #math-ph #math.DS #math.MP
paper · pdf · doi:10.48550/arxiv.0809.4389
11 pages
arxiv created 2008/09/25 · openalex publication_date 2008/09/25 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.