Work

Ergodicity of explicit logarithmic cocycles over IETs

Year: 2025

Type: article

Abstract: We prove ergodicity in a class of skew-product extensions of interval exchange transformations given by cocycles with logarithmic singularities. This, in particular, provides explicit examples of ergodic $${\mathbb {R}}$$ -extensions of minimal locally Hamiltonian flows with non-degenerate saddles in genus two. More generally, given any symmetric irreducible permutation, we show that for almost every choice of lengths, the skew-product built over the associated IET using a cocycle with symmetric logarithmic singularities that is odd when restricted to each of the exchanged intervals is ergodic.

Source: Mathematische Annalen

DOI: 10.1007/s00208-025-03246-y

Authors: P. Berk, F. Trujillo, C. Ulcigrai

Institutions: Nicolaus Copernicus University, Centre de Recerca Matemàtica, University of Zurich

Language: English

Topic: Mathematical Dynamics and Fractals

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,190

Funders: National Science Foundation, Schweizerischer Nationalfonds zur Förderung der Wissenschaftlichen Forschung, Universität Zürich, Agencia Estatal de Investigación