Spectrum of the Poincaré map for periodic reflecting rays in generic domains

DOI10.1007/BF01161919zbMath0673.58035MaRDI QIDQ1120878

Vesselin Petkov, Latchezar Stoyanov

Publication date: 1987

Published in: Mathematische Zeitschrift (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/173852

zbMATH Keywords

scatteringbilliardsjetsgeneric propertiesprobleminverse spectralKupka-Smale type theoremperiodic ray

Mathematics Subject Classification ID

Spectral problems; spectral geometry; scattering theory on manifolds (58J50) Ergodic theorems, spectral theory, Markov operators (37A30) Local and nonlocal bifurcation theory for dynamical systems (37G99)

Related Items (9)

Convex billiards on convex spheres ⋮ Singularities of the Scattering Kernel and Scattering Invariants for Several Strictly Convex Obstacles ⋮ Unnamed Item ⋮ Billiards in generic convex bodies have positive topological entropy ⋮ Quantum ergodic restriction theorems. I: Interior hypersurfaces in domains with ergodic billiards ⋮ On the number of periodic reflecting rays in generic domains ⋮ Equidistribution of phase shifts in semiclassical potential scattering ⋮ A bumpy metric theorem and the Poisson relation for generic strictly convex domains ⋮ Expansiveness and hyperbolicity in convex billiards

Cites Work

• The Poisson summation formula for manifolds with boundary
• Sojourn times and asymptotic properties of the scattering matrix
• Generic properties of geodesic flows
• Mechanical and gradient systems; local perturbations and generic properties
• Periodic geodesics of generic nonconvex domains in 𝐑² and the Poisson relation
• On the number of periodic reflecting rays in generic domains
• High frequency asymptotics of the scattering amplitude for non-convex bodies
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