Periodical
Topological approach to the generalized $ n$-centre problem
| العنوان: | Topological approach to the generalized $ n$-centre problem |
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| المؤلفون: | Bolotin, S V, Kozlov, V V |
| المصدر: | Russian Mathematical Surveys; June 2017, Vol. 72 Issue: 3 p451-478, 28p |
| مستخلص: | This paper considers a natural Hamiltonian system with two degrees of freedom and Hamiltonian $ H=\Vert p\Vert^2/2+V(q)$. The configuration space $ M$ is a closed surface (for non-compact $ M$ certain conditions at infinity are required). It is well known that if the potential energy $ V$ has $ n>2\chi(M)$ Newtonian singularities, then the system is not integrable and has positive topological entropy on the energy level $ H=h>\sup V$. This result is generalized here to the case when the potential energy has several singular points $ a_j$ of type $ V(q)\sim {-}\operatorname{dist}(q,a_j)^{-\alpha_j}$. Let $ A_k=2-2k^{-1}$, $ k\in\mathbb{N}$, and let $ n_k$ be the number of singular points with $ A_k\leqslant \alpha_j |
| قاعدة البيانات: | Supplemental Index |
| تدمد: | 00360279 14684829 |
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