Embedding and Renormalisation of a cone exchange transformation

Ana Rodrigues (University of Exeter)

Frank Adams 1,

Piecewise Isometries (PWIs) are higher dimensional generalizations of interval exchange transformations (IETs) that have highly complex and little understood behaviour. In this talk I will introduce a new family of piecewise isometries and renormalize its first return map to a subset of its partition. This implies in particular the existence of infinitely many periodic islands for this map as well as non ergodicity close to the origin. 
(This is joint work with P. Peres)

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