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Paper ‘Non-uniquely ergodic foliations of thin type’

A part of my Ph.D. thesis has been published via the following paper.

Reiner Martin, Non-uniquely ergodic foliations of thin type. Ergodic Theory and Dynamical Systems 17, No. 3, 667-674 (1997).

Keywords

Ergodic foliation; thin type. AMS Classification: 57R30 Foliations, geometric theory; 57M07 Topological methods in group theory; 20E08 Groups acting on trees.

Abstract

We construct a minimal foliation of thin type which is not uniquely ergodic. The notion of thin type relates to Rips’ classification of foliations on 2-complexes.

Quoted in

• Brian Mann, Patrick Reynolds, Constructing non-uniquely ergodic arational trees, arXiv:1311.1771
• Ivan Dynnikov, Alexandra Skripchenko, On typical leaves of a measured foliated 2-complex of thin type, arXiv:1309.4884 (published in V. M. Buchstaber, B. A. Dubrovin, I. M. Krichever, Topology, Geometry, Integrable Systems, and Mathematical Physics: Novikov’s Seminar 2012-2014)