This article is cited in 13 papers

Non-integrability of restricted two body problems in constant curvature spaces

A. J. Maciejewski^a, M. Przybylska<sup>bc

a</sup> Institute of Astronomy, University of Zielona Góra, Podgórna 50, PL-65–246 Zielona Góra, Poland
^b INRIA, Projet Café, 2004, Route des Lucioles, B. P. 93, 06902 Sophia Antipolis Cedex, France
^c Toruń Centre for Astronomy, N. Copernicus University, Gagarina 11, PL-87–100 Toruń, Poland

Abstract: We consider a restricted problem of two bodies in constant curvature spaces. The Newton and Hooke interactions between bodies are considered. For both types of interactions, we prove the non-integrability of this problem in spaces with constant non-zero curvature. Our proof is based on the Morales–Ramis theory.

MSC: 37J30, 70H07, 34M35

Received: 18.11.2003

Language: English

DOI: 10.1070/RD2003v008n04ABEH000254

Bibliographic databases:

• 
• 
•