Quasiperiodic motion in the billiard problem with a softened boundary

Research output: Contribution to journalArticlepeer-review


The motion of a classical particle in a convex plane region with softened boundary is considered. The Kolmogorov-Arnol'd-Moser theory is applied to detect "whispering gallery" trajectories, i.e., solutions staying near the boundary. It turns out that the large energy solutions starting near the boundary are quasiperiodic and stay there for all time filling out the invariant tori in the phase space, under some regularity conditions on the force repelling the particle from the boundary. The same technique is applied to the analysis of propagation of a skew light ray through the optical fiber with nonuniform core. It is shown that the majority of skew light rays starting near the boundary of the fiber stay there for all time under some restrictions on the refraction index.

Original languageEnglish (US)
Pages (from-to)4393-4396
Number of pages4
JournalPhysical review letters
Issue number24
StatePublished - 1995
Externally publishedYes

ASJC Scopus subject areas

  • Physics and Astronomy(all)


Dive into the research topics of 'Quasiperiodic motion in the billiard problem with a softened boundary'. Together they form a unique fingerprint.

Cite this