Fitting Invariant Curves on Billiard Tables and the Birkhoff-Herman TheoremIV International Symposium on Hamiltonian Systems and Celestial Mechanics, HAMSYS-2001 (2004)
A two-dimensional billiard table is geometrically integrable when the phase space is foliated by continuous invariant curves. When an integrable planar domain has a C⁴ boundary with strictly positive curvature, a neighborhood of the boundary is foliated by invariant circles. This family of invariant circles can lose convexity only after developing a singularity and if it developes a singularity, the boundary contains a segment of an ellipse. An important role in this result is played by the Birkhoff-Herman thoerem which shows that differentiability of enveloped curves cannot be lost without a change in homotopy type.
- Billiard map,
- Invariant curves,
- Birkhoff-Herman theormen
Publication DateJanuary 1, 2004
Citation InformationEdoh Y. Amiran. "Fitting Invariant Curves on Billiard Tables and the Birkhoff-Herman Theorem" IV International Symposium on Hamiltonian Systems and Celestial Mechanics, HAMSYS-2001 (2004)
Available at: http://works.bepress.com/edoh_amiran/7/