Billiard books model all three-dimensional bifurcations of integrable Hamiltonian systems. (English. Russian original) Zbl 1408.37098
Sb. Math. 209, No. 12, 1690-1727 (2018); translation from Mat. Sb. 209, No. 12, 17-56 (2018).
Summary: We introduce a new class of billiards – billiard books, which are integrable Hamiltonian systems. It turns out that for any nondegenerate three-dimensional bifurcation (3-atom), a billiard book can be algorithmically constructed in which such a bifurcation appears. Consequently, any integrable Hamiltonian nondegenerate dynamical system with two degrees of freedom can be modelled in some neighbourhood of a critical leaf of the Liouville foliation in the iso-energy 3-manifold by a billiard.
MSC:
| 37J35 | Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests |
| 37G10 | Bifurcations of singular points in dynamical systems |
| 37J20 | Bifurcation problems for finite-dimensional Hamiltonian and Lagrangian systems |
| 70E40 | Integrable cases of motion in rigid body dynamics |
| 37J05 | Relations of dynamical systems with symplectic geometry and topology (MSC2010) |
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