Abstract
Assume that the planar region Ω has aC1 boundary ∂Ω and is strictly convex in the sense that the tangent angle determines a point on the boundary. The lengths of invariant circles for the billiard ball map (or caustics) accumulate on |∂Ω|. It follows from direct calculations and from relations between the lengths of invariant circles and the lengths of trajectories of the billiard ball map that under mild assumptions on the lengths of some geodesics the region satisfies the strong noncoincidence condition. This condition plays a role in recovering the lengths of closed geodesics from the spectrum of the Laplacian. Asymptotics for the lengths of invariant circles and an application to ellipses are discussed. In addition; some examples regarding strong non coincidence are given.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
