Conserved Quantity for Fractional Constrained Hamiltonian System

Symmetric multistep methods for constrained Hamiltonian systems

A method of choice for the long-time integration of constrained Hamiltonians systems is the Rattle algorithm. It is symmetric, symplectic, and nearly preserves the Hamiltonian, but it is only of order two and thus not efficient for high accuracy requirements. In this article we prove that certain symmetric linear multistep methods have the same qualitative behavior and can achieve an arbitraril...

Evidence for a Conserved Quantity in Human Mobility

Recent seminal works on human mobility have shown that individuals constantly exploit a small set of repeatedly visited locations. A concurrent literature has emphasized the explorative nature of human behavior, showing that the number of visited places grows steadily over time. How to reconcile these seemingly contradicting facts remains an open question. Here, we analyze high-resolution multi...

Possible conserved quantity for the Hénon-Heiles problem.

Lagrangian and Hamiltonian Mechanics with Fractional Derivatives

In this paper we discuss the fractional extention of classical Lagrangian and Hamiltonian mechanics. We give a view of the mathematical tools associated with fractional calculus as well as a description of some applications.

Fractional generalization of gradient and Hamiltonian systems

We consider a fractional generalization of Hamiltonian and gradient systems. We use differential forms and exterior derivatives of fractional orders. We derive fractional generalization of Helmholtz conditions for phase space. Examples of fractional gradient and Hamiltonian systems are considered. The stationary states for these systems are derived. PACS numbers: 45.20.−d, 05.45.−a