Astronomy and Astrophysics – Astronomy
Scientific paper
Jan 2011
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2011cemda.109....1l&link_type=abstract
Celestial Mechanics and Dynamical Astronomy, Volume 109, Issue 1, pp.1-12
Astronomy and Astrophysics
Astronomy
3
Scientific paper
We show that the Hénon-Heiles system with Hamiltonian {H=frac12(y_1^2+y_2^2)+frac12(ax_1^2+bx_2^2)+frac13dx_2^3+cx_1^2x_2} is integrable in Liouvillian sense (i.e., the existence of an additional first integral) if and only if c = 0; or {frac dc=1, a=b; or frac dc=6, a, b} arbitrary; or {frac dc=16, b=16a}. Therefore, we get a complete classification of the Hénon-Heiles system in sense of integrability and non-integrability.
Li Wenlei
Shi Shaoyun
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