The Hénon-Heiles system as part of an integrable system grable system

Lesfari, A.


Abstract:

In this paper, we construct a new completely integrable system. This system is an instance of a master system of differential equations in 5 unknowns having 3 quartics constants of motion.We find via the Painlev analysis the principal balances of the hamiltonian field defined by the hamiltonian. Consequently, the system in question is algebraically integrable. A careful analysis of this system reveals an intimate rational relationship with a special case of the well known H�non-Heiles system. The latter admits asymptotic solutions with fractional powers in t and depending on 3 free parameters. As a consequence, this system is algebraically completely integrable in the generalized sense.

Volume: 6 | Issue: 3

Pages: 24-31

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