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arXiv · 2312.17405

Renormalization of Translated Cone Exchange Transformations

Noah Cockram·Peter Ashwin·Ana Rodrigues
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Abstract

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.

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Noah Cockram, Peter Ashwin, Ana Rodrigues. 2023-12-29. Renormalization of Translated Cone Exchange Transformations. https://arxiv.org/abs/2312.17405

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