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
Abstract:
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.References
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Additional Information
- Josué Damasceno
- Affiliation: Departamento de Matemática, Universidade Federal de Ouro Preto, 35.400–000, Ouro Preto, Brazil
- Email: josue@iceb.ufop.br
- Mario J. Dias Carneiro
- Affiliation: Departamento de Matemática, ICEx, Universidade Federal de Minas Gerais, 30.123–970, Belo Horizonte, Brazil
- Email: carneiro@mat.ufmg.br
- Rafael Ramírez-Ros
- Affiliation: Departament de Matemàtiques, Universitat Politècnica de Catalunya, Diagonal 647, 08028 Barcelona, Spain
- Email: rafael.ramirez@upc.edu
- 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: https://doi.org/10.1090/proc/13351
- MathSciNet review: 3577872