Geodesic
Evolutionary force billiards
Izvestiya. Mathematics , Tome 86 (2022) no. 5, pp. 943-979

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A new class of integrable billiards has been introduced: evolutionary force billiards. They depend on a parameter and change their topology as energy (time) increases. It has been proved that they realize some important integrable systems with two degrees of freedom on the entire symplectic four-dimensional phase manifold at a time, rather than on only individual isoenergy 3-surfaces. For instance, this occurs in the Euler and Lagrange cases. It has also been proved that these two well-known systems are “billiard-equivalent”, despite the fact that the former one is square integrable, and the latter one allows a linear integral.
Keywords: integrable system, evolutionary force billiards.
Mots-clés : billiard book, Fomenko–Zieschang invariant, Liouville equivalence 
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     author = {A. T. Fomenko and V. V. Vedyushkina},
     title = {Evolutionary force billiards},
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A. T. Fomenko; V. V. Vedyushkina. Evolutionary force billiards. Izvestiya. Mathematics , Tome 86 (2022) no. 5, pp. 943-979. http://geodesic.mathdoc.fr/item/IM2_2022_86_5_a6/