Related papers: On continuous orbit equivalence rigidity for virtu…

We show that the presence of a non-contractible one-periodic orbit of a Hamiltonian diffeomorphism of a connected closed symplectic manifold $(M,\omega)$ implies the existence of infinitely many non-contractible simple periodic orbits,…

We introduce a notion of uniformly continuous orbit equivalence as a subequivalence relation of continuous orbit equivalence of one-sided topological Markov shifts. It is described in terms of gauge actions on the associated Cuntz-Krieger…

We consider finitely generated groups of real-analytic circle diffeomorphisms. We show that if such a group admits an exceptional minimal set (i.e., a minimal invariant Cantor set), then its Lebesgue measure is zero; moreover, there are…

Since the work of Ornstein and Weiss in 1987 (J. Analyse Math. 48 (1987)) it has been understood that the natural category for classical ergodic theory would be probability measure preserving actions of discrete amenable groups. A…

We study hyperpolar actions on reducible symmetric spaces of the compact type. Our main result is that an indecomposable hyperpolar action on a symmetric space of the compact type is orbit equivalent to a Hermann action or of cohomogeneity…

Previous work showed that all Bernoulli shifts over a free group are orbit-equivalent. This result is strengthened here by replacing Bernoulli shifts with the wider class of properly ergodic countable state Markov chains over a free group.…

The existence of hyperbolic orbits is proved for a class of singular Hamiltonian systems $\ddot{u}(t)+\nabla V(u(t))=0$ by taking limit for a sequence of periodic solutions which are the variational minimizers of Lagrangian actions.

We associate to every action of a Polish group on a standard probability space a Polish group that we call the orbit full group. For discrete groups, we recover the well-known full groups of pmp equivalence relations equipped with the…

We give an elementary proof for Lewis Bowen's theorem saying that two Bernoulli actions of two free groups, each having arbitrary base probability spaces, are stably orbit equivalent. Our methods also show that for all compact groups K and…

Let $G$ be a group acting freely, properly discontinuously and cellularly on a finite dimensional $C$W-complex $\Sigma(2n)$ which has the homotopy type of the $2n$- sphere $\mathbb{S}^{2n}$. Then, this action induces an action of the group…

We show that for every countable group, any sequence of approximate homomorphisms with values in permutations can be realized as the restriction of a sofic approximation of an orbit equivalence relation. Moreover, this orbit equivalence…

Let $\mathbb{G}$ be a compact Hausdorff group acting on a compact Hausdorff space $X$, $\alpha$ an irreducible $\mathbb{G}$-representation, and $C(X)$ the $C^*$-algebra of complex-valued continuous functions on $X$. We prove that the…

Given a topological group $ G $ and a Hausdorff topological group $ A $ on which $ G $ acts continuously and compatibly with the group operation of $ A $, we study the set of continuous cocycles of $ G $ with value in $ A $. This set is a…

We show that the topological rank of an orbit full group generated by an ergodic, probability measure-preserving free action of a non-discrete unimodular locally compact Polish group is two. For this, we use the existence of a cross section…

We show that the groupoids of two directed graphs are isomorphic if and only if the two graphs are orbit equivalent by an orbit equivalence that preserves isolated eventually periodic points. We also give a complete description of the…

We study properties of the Weyl pseudometric associated with an action of a countable amenable group on a compact metric space. We prove that the topological entropy and the number of minimal subsets of the closure of an orbit are both…

We consider orientation-preserving actions of a finite group G on the 3-sphere S^3 (and also on Euclidean space R^3). By the geometrization of finite group actions on 3-manifolds, if such an action is smooth then it is conjugate to an…

Given any strong orbit equivalence class of minimal Cantor systems and any cardinal number that is finite, countable, or the continuum, we show that there exists a minimal subshift within the given class whose number of asymptotic…

To any action of a compact quantum group on a von Neumann algebra which is a direct sum of factors we associate an equivalence relation corresponding to the partition of a space into orbits of the action. We show that in case all factors…

We prove that any polar action on a separable Hilbert space by a connected Hilbert Lie group does not have exceptional orbits. This generalizes a result of Berndt, Console and Olmos in the finite dimensional Euclidean case. As an…