Abstract
Piecewise rotations are natural generalizations of interval exchange maps. They appear naturally in the theory of digital filters, Hamiltonian systems and polygonal dual billiards. We construct a rational piecewise rotation system with three atoms for which the return time to one of the atoms is unbounded. We show that the return map gives rise to a self-similar structure of induced atoms. The constructions are based on the angle of rotation π/7. Moreover, we construct a continuous class of examples with an infinite number of periodic cells. These periodic cells alternate between two atoms and they form a self-similar structure. Our investigation here may be viewed as generalizations of results obtained by Boshernitzan and Caroll, as well as Adler, Kitchens and Tresser, Kahng, Lowenstein and others. The main tools in the investigation are algebraic computations in a cyclotomic field determined by fourteenth roots of unity.
Sign-in/Register to access full text options 
Free) 
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
