Superintegrability in the Manev Problem and its Real Form Dynamics

TL;DR

This paper explores the superintegrability of the Manev problem, revealing conditions for invariants and analyzing the real form dynamics, which are always superintegrable, along with symmetry algebra discussions.

Contribution

It introduces Ermanno-Bernoulli invariants for the Manev model and shows that real form dynamics are always superintegrable, expanding understanding of its symmetry properties.

Findings

Existence of Ermanno-Bernoulli invariants under certain conditions.

Real form dynamics of the Manev model are always superintegrable.

Discussion of symmetry algebras of the Manev model.

Abstract

We report here the existence of Ermanno-Bernoulli type invariants for the Manev model dynamics which may be viewed upon as remnants of Laplace-Runge-Lenz vector whose conservation is characteristic of the Kepler model. If the orbits are bounded these invariants exist only when a certain rationality condition is met and thus we have superintegrability only on a subset of initial values. We analyze real form dynamics of the Manev model and derive that it is always superintegrable. We also discuss the symmetry algebras of the Manev model and its real Hamiltonian form.