Geodesic
Normal forms of billiards
Žurnal matematičeskoj fiziki, analiza, geometrii, Tome 9 (2002) no. 4, pp. 663-685
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The theory for normal billiard forms as a new class of reversible dynamic systems with projective involution is created. The qualitative analysis is carried out for regular points of billiard mapping that are close to the cycles of arbitrary order and about the diagonal of symmetric phase space. 
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     author = {S. V. Naydenov and V. V. Yanovskii},
     title = {Normal forms of billiards},
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S. V. Naydenov; V. V. Yanovskii. Normal forms of billiards. Žurnal matematičeskoj fiziki, analiza, geometrii, Tome 9 (2002) no. 4, pp. 663-685. http://geodesic.mathdoc.fr/item/JMAG_2002_9_4_a8/