Normal Form, Lie-Poisson Structure and Reduction for the Henon-Heiles System

Details Normal Form, Lie-Poisson Structure and Reduction for the Henon-Heiles System Normal Form, Lie-Poisson Structure and Reduction for the Henon-Heiles System

Jan 1996

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1996cemda..63..245k&link_type=abstract

Celestial Mechanics & Dynamical Astronomy, Volume 63, Issue 3-4, pp. 245-253

Astronomy and Astrophysics

Astronomy

Henon-Heiles System, Normal Form, Lie-Poisson Structure, Reduction

Scientific paper

The reduced Henon-Heiles system is investigated as a Hamiltonian dynamical system obtained by applying the normalization of the HamiltonianH=1/2(p {1/2}+p {2/2}+q {1/2}+q {2/2})+1/3μq {1/3}-q 1 q {2/2} to fourth-degree terms. The related equations of motion are bi-Hamiltonian and possess the Lie-Poisson structure. Each Lie-Poisson structure possesses an associated Casimir function. When reduced to level sets of these functions, the equations of motion take various symplectic forms. The various reductions give different coordinate representations of the solutions. These coordinate representations are used to seek the simplest representation of the solutions.

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