arXiv subjects

Simon Robert

Publications and source records attributed to Simon Robert.

2 recordsLinked to original sources

arXiv2021

From invariant measures to orbit equivalence, via locally finite groups

We give a new proof of a theorem of Giordano, Putnam and Skau characterizing orbit equivalence of minimal homeomorphisms of the Cantor space in terms of their sets of invariant Borel probability measures. The proof is based on a strengtehning of a theorem of Krieger concerning minimal actions of certain locally finite groups of homeomorphisms, and we also give a new proof of the Giordano--Putnam--Skau characterization of orbit equivalence for these actions.

math.DS↗

arXiv2020

Strong Orbit Equivalence in Cantor dynamics and simple locally finite groups

We study certain countable locally finite groups attached to minimal homeomorphisms, and prove that the isomorphism relation on simple, countable, locally finite groups is a universal relation arising from a Borel $S_\infty$-action. This work also provides a dynamical approach to a result of Giordano, Putnam and Skau characterizing strong orbit equivalence.

math.DS↗