Abstract

We consider the outer billiards map with contraction outside polygons. We construct a 1-parameter family of systems such that each system has an open set in which the dynamics are reduced to that of a piecewise contraction on the interval. Using the theory of rotation numbers, we deduce that every point inside the open set is asymptotic to either a single periodic orbit (rational case) or a Cantor set (irrational case). In particular, we deduce the existence of an attracting Cantor set for certain parameter values. Moreover, for a different choice of 1-parameter family, we prove that the system is uniquely ergodic; in particular, the entire domain is asymptotic to a single attractor.

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 call

Disclaimer: 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.