Regularisation by Hamiltonian extension

We consider the Kepler potential and its relatives \(q\mapsto -\|q\|^{-2(1-1/n)}\), \(n\in\mathbb{N}\) in arbitrary dimension \(d\). We derive a unique real-analytic symplectic extension of phase space on which the Hamiltonian flow is complete and still real-analytic.

Saved in:
Bibliographic Details
Published in:arXiv.org 2024-08
Main Author: Knauf, Andreas
Format: Article
Language:English
Subjects:
Regularization
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:We consider the Kepler potential and its relatives \(q\mapsto -\|q\|^{-2(1-1/n)}\), \(n\in\mathbb{N}\) in arbitrary dimension \(d\). We derive a unique real-analytic symplectic extension of phase space on which the Hamiltonian flow is complete and still real-analytic.
ISSN:2331-8422