On a canonical nine-body problem. Integrable Ermakov decomposition via reciprocal transformations

Abstract

Here, a recently introduced nine-body problem is shown to be decomposable via a novel class of reciprocal transformations into a set of integrable Ermakov systems. This Ermakov decomposition is exploited to construct more general integrable nine-body systems in which the canonical nine-body system is embedded.

Keywords:

• Many Body
• Ermakov
• Reciprocal

2000 Mathematics Subject Classification:

• MSC 37K10