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Bifurcation analysis of low resonant case of the generalized Hénon-Heiles system. (English) Zbl 1051.37002

Ganzha, Victor G. (ed.) et al., Computer algebra in scientific computing, CASC 2001. Proceedings of the 4th international workshop, Konstanz, Germany, September 22–26, 2001. Berlin: Springer (ISBN 3-540-42355-9). 167-175 (2001).
Summary: The paper describes a computer algebra application of the normal form method to bifurcation analysis of a low resonant case of the generalized Hénon-Heiles system. The behavior of all local families of periodic solutions in system parameters is determined. Corresponding approximated solutions are checked by a comparison with the numerical solutions of the system.
For the entire collection see [Zbl 0970.00027].

MSC:

37-04 Software, source code, etc. for problems pertaining to dynamical systems and ergodic theory
37G05 Normal forms for dynamical systems
68W30 Symbolic computation and algebraic computation
34C23 Bifurcation theory for ordinary differential equations
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