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Noah Cockram

Publications and source records attributed to Noah Cockram.

3 recordsLinked to original sources
arXiv2023

Renormalization of Translated Cone Exchange Transformations

In this paper, we investigate a class of non-invertible piecewise isometries on the upper half-plane known as Translated Cone Exchanges. These maps include a simple interval exchange on a boundary we call the baseline. We provide a geometric construction for the first return map to a neighbourhood of the vertex of the middle cone for a large class of parameters, then we show a recurrence in the first return map tied to Diophantine properties of the parameters, and subsequently prove the infinite renormalizability of the first return map for these parameters.

math.DS↗
arXiv2023

Construction of Invariant Curves for Some Piecewise Isometries

We establish conditions for the existence of a family of piecewise linear invariant curves in a two-parameter family of piecewise isometries on the upper half-plane known as Translated Cone Exchange Transformations. We show that these curves are embeddings of interval exchange transformations and give rise to layers of invariant regions. We also show the existence of a trapezoidal piecewise isometry for which the dynamics on the top and bottom edges are distinct 2-interval exchange transformations.

math.DS↗