39 citations · 104 across the 23 of their papers we have counts for
28 papers
Some aspects of topological dynamics of Polish groups (with an introduction to descriptive set theory)
Julien Melleray
The first part of these notes give an introduction to the theory of Polish group actions on compact Hausdorff spaces, leading up to a proof of the Kechris-Pestov-Todorcevic corresp…
Dense and comeager conjugacy classes in zero-dimensional dynamics
Michal Doucha, Julien Melleray, Todor Tsankov
Given a countable group , we initiate a systematic study of the Polish spaces of all minimal and topologically transitive actions of on the Cantor space by homeomorphisms, w…
Clopen type semigroups of actions on -dimensional compact spaces
Julien Melleray
We investigate some properties of the clopen type semigroup of an action of a countable group on a compact, -dimensional, Hausdorff space X. We discuss some characterizations of…
A topometric Effros theorem
Itaï Ben Yaacov, Julien Melleray
Given a continuous and isometric action of a Polish group on an adequate Polish topometric space and , we find a necessary and sufficient condition for $\ove…
From invariant measures to orbit equivalence, via locally finite groups
Julien Melleray, Simon Robert
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 Bor…
Generic properties of homeomorphisms preserving a given dynamical simplex
Julien Melleray
Given a dynamical simplex on a Cantor space , we consider the set of all homeomorphisms of which preserve all elements of and have no nontrivial clopen invar…