Analytical Non-integrability of the Truncated Two Fixed Centres Problem in the Symmetric Case

✍ Scribed by Maylis Irigoyen

• Publisher: Elsevier Science
• Year: 1996
• Tongue: English
• Weight: 312 KB
• Volume: 131
• Category: Article
• ISSN: 0022-0396
• DOI: 10.1006/jdeq.1996.0164

✦ Synopsis

The Problem of two fixed centres is an integrable Hamiltonian system. If one truncates the Taylor expansion of the potential of this problem (in the symmetric case) at any order 3, we prove that one obtains a system which does not admit any first integral, meromorphic and functionally independent of the energy and the angular momentum. The proof is mainly founded on the criterion of nonintegrability for homogeneous potentials, derived by Yoshida from Ziglin's theorem. Then we use this result to prove that the Vinti Problem, truncated at any order 3, is analytically non-integrable.