Density of convex billiards with rational caustics
Kaloshin V, Zhang K. 2018. Density of convex billiards with rational caustics. Nonlinearity. 31(11), 5214–5234.
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Author
Kaloshin, VadimISTA 
;
Zhang, Ke
;
Zhang, KeAbstract
We show that in the space of all convex billiard boundaries, the set of boundaries with rational caustics is dense. More precisely, the set of billiard boundaries with caustics of rotation number 1/q is polynomially sense in the smooth case, and exponentially dense in the analytic case.
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Publishing Year
Date Published
2018-10-15
Journal Title
Nonlinearity
Volume
31
Issue
11
Page
5214-5234
IST-REx-ID
Cite this
Kaloshin V, Zhang K. Density of convex billiards with rational caustics. Nonlinearity. 2018;31(11):5214-5234. doi:10.1088/1361-6544/aadc12
Kaloshin, V., & Zhang, K. (2018). Density of convex billiards with rational caustics. Nonlinearity. IOP Publishing. https://doi.org/10.1088/1361-6544/aadc12
Kaloshin, Vadim, and Ke Zhang. “Density of Convex Billiards with Rational Caustics.” Nonlinearity. IOP Publishing, 2018. https://doi.org/10.1088/1361-6544/aadc12.
V. Kaloshin and K. Zhang, “Density of convex billiards with rational caustics,” Nonlinearity, vol. 31, no. 11. IOP Publishing, pp. 5214–5234, 2018.
Kaloshin V, Zhang K. 2018. Density of convex billiards with rational caustics. Nonlinearity. 31(11), 5214–5234.
Kaloshin, Vadim, and Ke Zhang. “Density of Convex Billiards with Rational Caustics.” Nonlinearity, vol. 31, no. 11, IOP Publishing, 2018, pp. 5214–34, doi:10.1088/1361-6544/aadc12.
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