English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

We consider algebraic geometrical properties of the integrable billiard on aquadric Q with elastic impacts along another quadric confocal to Q. Theseproperties are in sharp contrast with those of the ellipsoidal Birkhoffbilliards. Namely, generic complex invariant manifolds are not Abelianvarieties, and the billiard map is no more algebraic. A Poncelet-like theoremfor such system is known. We give explicit sufficient conditions both forclosed geodesics and periodic billiard orbits on Q and discuss their relationwith the elliptic KdV solutions and elliptic Calogero systemComment: 23 pages, Latex, 1 figure Postscrip

Closed Geodesics and Billiards on Quadrics Related to Elliptic KdV Solutions