Geodesic
Singularities of integrable Liouville systems, reduction of integrals to lower degree and topological billiards: recent results
Theoretical and applied mechanics, Tome 46 (2019) no. 1.

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In the paper we present the new results in the theory of integrable Hamiltonian systems with two degrees of freedom and topological billiards. The results are obtained by the authors, their students, and participants of scientific seminars of the Department of Differential Geometry and Applications, Faculty of Mathematics and Mechanics at Lomonosov Moscow State University.
Keywords: integrable systems, topological billiards, Liouville equivalence, Minkowski space, geodesic flows, Fomenko--Zieschang invariants 
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     author = {A. T. Fomenko and V. V. Vedyushkina},
     title = {Singularities of integrable {Liouville} systems, reduction of integrals to lower degree and topological billiards: recent results},
     journal = {Theoretical and applied mechanics},
     pages = {47 - 63},
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A. T. Fomenko; V. V. Vedyushkina. Singularities of integrable Liouville systems, reduction of integrals to lower degree and topological billiards: recent results. Theoretical and applied mechanics, Tome 46 (2019) no. 1. http://geodesic.mathdoc.fr/item/TAM_2019_46_1_a4/