A Non-Concentration Estimate for Partially Rectangular Billiards

A Non-concentration Estimate for Partially Rectangular Billiards

We consider quasimodes on planar domains with a partially rectangular boundary. We prove that for any ǫ0 > 0, an O(λ0 ) quasimode must have L mass in the “wings” (in phase space) bounded below by λ for any δ > 0. The proof uses the author’s recent work on 0-Gevrey smooth domains to approximate quasimodes on C domains. There is an improvement for C and C domains.

Resonant phenomena in slowly perturbed rectangular billiards

We consider a slowly rotating rectangular billiard with slowly moving borders. We use methods of the canonical perturbation theory to describe the dynamics of a billiard particle. In the process of slow evolution certain resonance conditions can be satisfied. We study the phenomena of scattering on a resonance and capture into a resonance. These phenomena lead to destruction of adiabatic invari...

Escape orbits for non-compact flat billiards.

It is proven that, under some conditions on f, the non-compact flat billiard Omega={(x,y) in R(0) (+)xR(0) (+); 0</=y</=f(x)} has no orbits going directly to + infinity. The relevance of such sufficient conditions is discussed. (c) 1996 American Institute of Physics.

Energy decay for damped wave equations on partially rectangular domains

We consider the wave equation with a damping term on a partially rectangular planar domain, assuming that the damping is concentrated close to the non-rectangular part of the domain. Polynomial decay estimates for the energy of the solution are established.

Multilevel Tiling for Non-rectangular Iteration Spaces