Work

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

Year: 2025

Type: article

Abstract: We prove that almost every interval exchange transformation, with an associated translation surface of genus $g\geq 2$ , 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.

Source: Ergodic Theory and Dynamical Systems

DOI: 10.1017/etds.2024.53

Authors: PEDRO PERES, ANA RODRIGUES

Institutions: University of Exeter, University of Évora, Centro de Investigação em Matemática e Aplicações

Language: English

Topic: Mathematical Dynamics and Fractals

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

OpenAlex ID: W4407894376

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Cites: 24

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Related to: 10