Invariant Tori for the Billiard Ball Map

DOI10.2307/2001453zbMath0686.58037OpenAlexW4235163631MaRDI QIDQ4204852

Valery Kovachev, Georgi S. Popov

Publication date: 1990

Full work available at URL: https://doi.org/10.2307/2001453

zbMATH Keywords

invariant torisymplectic diffeomorphismelliptic closed geodesicbilliard ball map

Mathematics Subject Classification ID

Spectral problems; spectral geometry; scattering theory on manifolds (58J50)

Related Items (10)

Invariants of the length spectrum and spectral invariants of planar convex domains ⋮ Wire billiards, the first steps ⋮ Another Billiard problem ⋮ Arnold diffusion in multidimensional convex billiards ⋮ An \(n\) center problem as an example of a geodesic billiard map with singularities: Poincaré maps and dynamics ⋮ Aubry-Mather theory and the inverse spectral problem for planar convex domains ⋮ The quantum Sabine law for resonances in transmission problems ⋮ On some invariants of Birkhoff billiards under conjugacy ⋮ Length spectrum invariants of Riemannian manifolds ⋮ Computing Mather's \(\beta\)-function for Birkhoff billiards

Cites Work

• Spectral invariants of convex planar regions
• Equivalence of glancing hyper-surfaces
• Integrability of hamiltonian systems on cantor sets
• The inverse function theorem of Nash and Moser
• Riemannian geometry
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