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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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The billiard inside an ellipse deformed by the curvature flow
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by Josué Damasceno, Mario J. Dias Carneiro and Rafael Ramírez-Ros PDF
Proc. Amer. Math. Soc. 145 (2017), 705-719 Request permission


The billiard dynamics inside an ellipse is integrable. It has zero topological entropy, four separatrices in the phase space, and a continuous family of convex caustics: the confocal ellipses. We prove that the curvature flow destroys the integrability, increases the topological entropy, splits the separatrices in a transverse way, and breaks all resonant convex caustics.
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Additional Information
  • Josué Damasceno
  • Affiliation: Departamento de Matemática, Universidade Federal de Ouro Preto, 35.400–000, Ouro Preto, Brazil
  • Email:
  • Mario J. Dias Carneiro
  • Affiliation: Departamento de Matemática, ICEx, Universidade Federal de Minas Gerais, 30.123–970, Belo Horizonte, Brazil
  • Email:
  • Rafael Ramírez-Ros
  • Affiliation: Departament de Matemàtiques, Universitat Politècnica de Catalunya, Diagonal 647, 08028 Barcelona, Spain
  • Email:
  • Received by editor(s): November 4, 2015
  • Received by editor(s) in revised form: April 6, 2016
  • Published electronically: September 29, 2016
  • Additional Notes: The third author was supported in part by CUR-DIUE Grant 2014SGR504 (Catalonia) and MINECO-FEDER Grant MTM2015-65715-P (Spain).
  • Communicated by: Yingfei Yi
  • © Copyright 2016 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 145 (2017), 705-719
  • MSC (2010): Primary 37E40, 37J45, 37B40, 53C44
  • DOI:
  • MathSciNet review: 3577872