We consider Dirichlet eigenfunctions uλ of the Bunimovich stadium S, satisfying (∆− λ2)uλ = 0. Write S = R ∪W where R is the central rectangle and W denotes the “wings,” i.e. the two semicircular regions. It is a topic of current interest in quantum theory to know whether eigenfunctions can concentrate in R as λ → ∞. We obtain a lower bound Cλ on the L mass of uλ in W , assuming that uλ itself ...

In order to design a reasonable pedestrian evacuation and exclude the security risks in large stadiums, this thesis proposes the research of security model of evacuation in stadiums combined with multi-agent and cellular automata. The research is based on cellular automata model and the process makes extended analysis to the cell’s behavior of autologous, and then it makes simulation experiment...

We investigate the existence of elliptic islands for a special family of periodic orbits of a twoparameter family of maps Ta,h, corresponding to the billiard problem on the elliptical stadium. The hyperbolic character of those orbits were studied in [2] for 1 < a < √ 2 and here we look for the elliptical character for every a > 1. We prove that, for a < √ 2, the lower bound for chaos h = H(a) f...

We construct a well ordered symbolic dynamics plane for the stadium billiard. In this symbolic plane the forbidden and the allowed orbits are separated by a monotone pruning front, and allowed orbits can be systematically generated by sequences of approximate finite grammars. 1 ‡ Permanent address: Phys Dep., University of Oslo, Box 1048, Blindern, N-0316 Oslo