Geodesic
Billiard books model all three-dimensional bifurcations of integrable Hamiltonian systems
Sbornik. Mathematics, Tome 209 (2018) no. 12, pp. 1690-1727

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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. Bibliography: 25 titles.
Keywords: integrable system
Mots-clés : billiard, Liouville equivalence, Fomenko-Zieschang invariant. 
@article{SM_2018_209_12_a1,
     author = {V. V. Vedyushkina and I. S. Kharcheva},
     title = {Billiard books model all three-dimensional bifurcations of integrable {Hamiltonian} systems},
     journal = {Sbornik. Mathematics},
     pages = {1690--1727},
     publisher = {mathdoc},
     volume = {209},
     number = {12},
     year = {2018},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_2018_209_12_a1/}
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V. V. Vedyushkina; I. S. Kharcheva. Billiard books model all three-dimensional bifurcations of integrable Hamiltonian systems. Sbornik. Mathematics, Tome 209 (2018) no. 12, pp. 1690-1727. http://geodesic.mathdoc.fr/item/SM_2018_209_12_a1/