Fractional embeddings and stochastic time

TL;DR

This paper explores how fractional embeddings influence Hamiltonian systems with long-tail recurrence time distributions, connecting Stanislavsky's fractional formalism to a causal least action principle.

Contribution

It demonstrates that Stanislavsky's fractional Hamiltonian formalism can be derived from fractional embedding theory and a specific least action principle.

Findings

Fractional embedding theory can reproduce Stanislavsky's formalism.

Fractional Hamiltonian systems follow a causal least action principle.

The approach clarifies the coherence of fractional embeddings in Hamiltonian dynamics.

Abstract

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.