Existence of non trivial embeddings of interval exchange transformations into piecewise isometries

• Author(s): Peres, Pedro ; Rodrigues, Ana
• Date: 2025
• Persistent ID: http://hdl.handle.net/10174/38260
• Origin: Repositório Científico da Universidade de Évora
• Document Type: Journal article
• Language: Portuguese

Description

We prove that almost every interval exchange transformation, with an associated translation surface of genus ≥2 , can be non-trivially and isometrically embedded in a family of piecewise isometries. In particular, this proves the existence of invariant curves for piecewise isometries, reminiscent of Kolmogorov–Arnold–Moser (KAM) curves for area-preserving maps, which are not unions of circle arcs or line segments.