Hamiltonian Dynamics for the Kepler Problem in a Deformed Phase Space

TL;DR

This paper explores the Hamiltonian dynamics of the Kepler problem within a deformed phase space, identifying integrals of motion and quasi-bi-Hamiltonian structures, advancing understanding of orbital mechanics in modified geometries.

Contribution

It introduces a novel analysis of the Kepler problem in a deformed phase space, including the construction of recursion operators and the study of quasi-bi-Hamiltonian structures.

Findings

Construction of recursion operators for the deformed phase space

Identification of integrals of motion including the Laplace-Runge-Lenz vector

Existence of quasi-bi-Hamiltonian structures in the system

Abstract

This work addresses the Hamiltonian dynamics of the Kepler problem in a deformed phase space, by considering the equatorial orbit. The recursion operators are constructed and used to compute the integrals of motion. The same investigation is performed with the introduction of the Laplace-Runge-Lenz vector. The existence of quasi-bi-Hamiltonian structures is also elucidated. Related properties are studied.