Geodesic
Invariant Distributions in Systems with Elastic Reflections
Teoretičeskaâ i matematičeskaâ fizika, Tome 130 (2002) no. 2, pp. 301-319

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We derive equations for invariant distributions of billiards as invertible (measure-preserving) dynamic systems in a symmetric phase space and find their solutions. We introduce and investigate invariant measures for the complete and contracted descriptions and establish the relation between them. 
@article{TMF_2002_130_2_a6,
     author = {S. V. Naydenov and V. V. Yanovskii},
     title = {Invariant {Distributions} in {Systems} with {Elastic} {Reflections}},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {301--319},
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     volume = {130},
     number = {2},
     year = {2002},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2002_130_2_a6/}
}
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S. V. Naydenov; V. V. Yanovskii. Invariant Distributions in Systems with Elastic Reflections. Teoretičeskaâ i matematičeskaâ fizika, Tome 130 (2002) no. 2, pp. 301-319. http://geodesic.mathdoc.fr/item/TMF_2002_130_2_a6/