Renormalization of translated cone exchange transformations

• Autor(es): Cockram, Noah ; Ashwin, Peter ; Rodrigues, Ana
• Data: 2025
• Identificador Persistente: http://hdl.handle.net/10174/38262
• Origem: Repositório Científico da Universidade de Évora
• Tipo de Documento: Artigo científico
• Idioma: Português

Descrição

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.