Noah Cockram: Renormalizability of Translated Cone Exchanges

Abstract:

Piecewise Isometries are a natural generalisation of Interval Exchange Transformations which appear in the study of overflow oscillations in lossless digital filters, dual billiards, as well as in kicked Hamiltonian systems whose phase spaces resemble circle packings. Despite having no expansion or contraction and zero topological entropy, can still nevertheless exhibit infinitely renormalizable behaviour, orbits with periodic encodings of arbitrarily high period, and sometimes seemingly positive measure sets of aperiodically encoded orbits. In this talk, we will discuss renormalizability in a class of piecewise isometries known as Translated Cone Exchanges, and present an example of a continuous, piecewise-linear invariant curve which is an embedding of a 4-IET.