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2013
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# Roberto Markarian

Montevideo, Uruguay
Instituto de Matemática y Estadística “Prof. Ing. Rafael Laguardia” (IMERL), Facultad de Ingeniería, Universidad de la República

## Publications:

 Del Magno G., Markarian R. Singular Sets of Planar Hyperbolic Billiards are Regular 2013, vol. 18, no. 4, pp.  425-452 Abstract Many planar hyperbolic billiards are conjectured to be ergodic. This paper represents a first step towards the proof of this conjecture. The Hopf argument is a standard technique for proving the ergodicity of a smooth hyperbolic system. Under additional hypotheses, this technique also applies to certain hyperbolic systems with singularities, including hyperbolic billiards. The supplementary hypotheses concern the subset of the phase space where the system fails to be $C^2$ differentiable. In this work, we give a detailed proof of one of these hypotheses for a large collection of planar hyperbolic billiards. Namely, we prove that the singular set and each of its iterations consist of a finite number of compact curves of class $C^2$ with finitely many intersection points. Keywords: hyperbolic billiards, ergodicity Citation: Del Magno G., Markarian R.,  Singular Sets of Planar Hyperbolic Billiards are Regular, Regular and Chaotic Dynamics, 2013, vol. 18, no. 4, pp. 425-452 DOI:10.1134/S1560354713040072