caa a22 4500 445862955 CHVBK 20180317145449.0 cr unu---uuuuu 170323e20110101xx s 000 0 eng 10.1007/s10569-010-9315-1 doi (NATIONALLICENCE)springer-10.1007/s10569-010-9315-1 Non-integrability of Hénon-Heiles system [Elektronische Daten] [Wenlei Li, Shaoyun Shi] 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 $${\frac dc=1, a=b; {\rm or}\, \frac dc=6, a, b}$$ 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. Springer Science+Business Media B.V., 2010 Non-integrability nationallicence Hénon-Heiles system nationallicence Morales-Ramis theory nationallicence Lamé equation nationallicence Higher order variational equations nationallicence Li Wenlei College of Mathematics, Jilin University, 130012, Changchun, People's Republic of China aut Shi Shaoyun Key Laboratory of Symbolic Computation and Knowledge Engineering of Ministry of Education, Jilin University, 130012, Changchun, People's Republic of China aut Celestial Mechanics and Dynamical Astronomy Springer Netherlands 109/1(2011-01-01), 1-12 0923-2958 109:1<1 2011 109 10569 https://doi.org/10.1007/s10569-010-9315-1 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s10569-010-9315-1 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Li Wenlei College of Mathematics, Jilin University, 130012, Changchun, People's Republic of China aut NATIONALLICENCE 700 1- Shi Shaoyun Key Laboratory of Symbolic Computation and Knowledge Engineering of Ministry of Education, Jilin University, 130012, Changchun, People's Republic of China aut NATIONALLICENCE 773 0- Celestial Mechanics and Dynamical Astronomy Springer Netherlands 109/1(2011-01-01), 1-12 0923-2958 109:1<1 2011 109 10569 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer