Translated Cone Exchanges and Invariant Curves
Lead Research Organisation:
UNIVERSITY OF EXETER
Department Name: Mathematics
Abstract
Although numerical experiments (see Ashwin P., Goetz A., Peres P., Rodrigues A., (2018). Embeddings of Interval Exchange Trans-
formations into Planar Piecewise Isometries, Ergodic Theory and Dynamical Systems, 1-27), support that the set ${\mathcal U(\lambda, \eta)$ should be nonempty for the parameters in consideration, it is not known whether this is true. Indeed, this
is related to one of the greatest open questions in this field of study: whether typical families of PWIs support embeddings of IETs.
formations into Planar Piecewise Isometries, Ergodic Theory and Dynamical Systems, 1-27), support that the set ${\mathcal U(\lambda, \eta)$ should be nonempty for the parameters in consideration, it is not known whether this is true. Indeed, this
is related to one of the greatest open questions in this field of study: whether typical families of PWIs support embeddings of IETs.
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