Document Zbl 1490.37038

On the circumcenters of triangular orbits in elliptic billiard. (English) Zbl 1490.37038

J. Dyn. Control Syst. 27, No. 4, 693-705 (2021).

The author studies elliptic-type billiards. In particular, he proves that the locus of circumcenters of all triangular orbits is an ellipse. To arrive at this result, the author uses refined methods in synthetic geometry such as complexified conics and reflection laws.

Reviewer: Emre Alkan (İstanbul)

Cited in 9 Documents

MSC:

37C83	Dynamical systems with singularities (billiards, etc.)
37C25	Fixed points and periodic points of dynamical systems; fixed-point index theory; local dynamics
37C55	Periodic and quasi-periodic flows and diffeomorphisms
51K10	Synthetic differential geometry

Keywords:

billiard; elliptic billiard; periodic orbits; triangular orbits; complex reflection law; circumcenters; ellipse; conic

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References:

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