Billiards in ellipses revisited

By A. Akopyan, Richard Evan Schwartz, Serge Tabachnikov. European Journal of Mathematics, 2020

49 citations recorded by the source corpus.

We prove some recent experimental observations of Dan Reznik concerning periodic billiard orbits in ellipses. For example, the sum of cosines of the angles of a periodic billiard polygon remains constant in the 1-parameter family of such polygons (that exist due to the Poncelet porism). In our proofs, we use geometric and complex analytic methods.

Subfields: Geometry and Topology, Mathematical Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/962bb277a41b28ac416868dae62460f23c87226e

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Geometry and Topology

1. Misha Bialy
2. Serge Tabachnikov
3. Sophie Morier-Genoud

In Mathematical Physics

1. Misha Bialy
2. Serge Tabachnikov

In Statistical and Nonlinear Physics

1. Misha Bialy
2. Serge Tabachnikov

Citations in the corpus

• Dan Reznik’s identities and more (2020, methodology): “e h( ) = 1=‘= q a2 1 cos2 + a2 2 sin 2 , as claimed. The billiard in ellipse is integrable, and the conserved quantity, called the Joachimsthal integral, is, in the above notation, jNjsin(see [6] or [2]). This can be written as J= sin( ) h( ) : This means that, along an invariant curve of the billia”