Billiards

A chaotic orbit. The physical orbit of the billiard. The points in the phase space. An orbit on an invariant curve near the caustic. The points in the phase space is near the equator A whisper galery orbit. Existence is known by KAM theory. The orbit is near the boundary of the phase space A KAM curve around an elliptic periodic orbit. The orbit in the phase space lies on invariant curves

Papers on families of billiards The l p billiard paper with M.Jeng was motivated by the problem of finding smooth Birkhoff billiards with positive Kolmogorov-Sinai entropy . A candidate is the algebraic table x 4 +y 4 = 1 animated above. The paper on tables of equal width was motivated by the Birkhoff-Poritsky conjecture asking whether ellipses are the only integrable billiards. The paper on string construction billiards with E. Gutkin is an applications of the theory of circle maps and shows exciting bifurcation phenomena . Also this is interesting in the context of the Birkhoff-Poritsky conjecture, where one has to understand exceptional caustics.

Java applets on Billiard by Victor J. Donnay

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