Non-integrability of a three-dimensional generalized Hénon-Heiles system
نویسندگان
چکیده
In recent paper Fakkousy et al. show that the 3D Hénon-Heiles system with Hamiltonian $$ H = \frac{1}{2} (p_1 ^2 + p_2 p_3 ^2) +\frac{1}{2} (A q_1 C q_2 B q_3 (\alpha \gamma ^2)q_3 \frac{\beta }{3}q_3 ^3 is integrable in sense of Liouville when $$\alpha , \frac{\alpha }{\beta } 1, A C$$ ; or \frac{1}{6}, B-arbitrary; \frac{1}{16}, C, \frac{A}{B} \frac{1}{16}$$ (and course, =\gamma =0$$ which case separable). It known second remains for A, arbitrary. Using Morales-Ramis theory, we prove there are no other cases integrability this system.
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ژورنال
عنوان ژورنال: European Physical Journal Plus
سال: 2021
ISSN: ['2190-5444']
DOI: https://doi.org/10.1140/epjp/s13360-021-02044-0