Related papers: Orbital Counting in Conjugacy Classes
Let $\gamma$ be a pseudo-Anosov homeomorphism and $X$ an element of the Teichmuller space of a genus $g$ surface. In this paper, we find asymptotics for the number of pseudo-Anosov homeomorphisms that are conjugate to $\gamma$ and the axis…
We consider a connected symplectic manifold $M$ acted on properly and in a Hamiltonian fashion by a connected Lie group $G$. Inspired to the recent paper \cite{gb2}, see also \cite{ch} and \cite{pacini}, we study Lagrangian orbits of…
It is proven that the orbit-equivalence class of any essentially free probability-measure-preserving action of a free group $G$ is weakly dense in the space of actions of $G$.
We show that the inverse limit and the orbit map commute for actions of compact groups on compact Hausdorff spaces.
We study the complexity of the classification problem of conjugacy on dynamical systems on some compact metrizable spaces. Especially we prove that the conjugacy equivalence relation of interval dynamical systems is Borel bireducible to…
In this paper, we study the asymptotics of several growth functions related to twisted conjugacy on virtually abelian groups. First, we study the twisted conjugacy growth function, which counts the number of twisted conjugacy classes…
In this paper we study chaotic behavior of actions of a countable discrete group acting on a compact metric space by self-homeomorphisms. For actions of a countable discrete group G, we introduce local weak mixing and Li-Yorke chaos; and…
In the first part of the paper, we introduce notions of asymptotic continuous orbit equivalence and asymptotic conjugacy in Smale spaces and characterize them in terms of their asymptotic Ruelle algebras with their dual actions. In the…
The present article presents geometric quantization on cotangent bundles as a special instance of Kirillov's orbit method. To this end, the cotangent bundle is realized as a coadjoint orbit of an infinite-dimensional Lie group constructed…
We use the combinatorial harmonic map theory to study the isometric actions of discrete groups on Hadamard spaces. Given a finitely generated group acting by automorphisms, properly discontinuously and cofinitely on a simplicial complex and…
In this paper we prove asymptotic estimates for closed geodesic loops on compact surfaces with no conjugate points. These generalize the classical counting results of Huber and Margulis and sector theorems for surfaces of strictly negative…
We study coadjoint orbitopes, i.e. convex hulls of coadjoint orbits of a compact Lie group. We show that all the faces of such an orbitope are exposed. The face structure is studied by means of the momentum map and it is shown that every…
We compute the number of orbit types for simply connected simple algebraic groups over algebraically closed fields as well as for compact simply connected simple Lie groups. We also compute the number of orbit types for the adjoint action…
We show that up to commensurability there are only finitely many cocompact arithmetic Kleinian groups generated by rotations. This implies, in particular, that there exist only finitely many conjugacy classes of cocompact two generated…
We classify the connected orientable 2-manifolds whose mapping class groups have a dense conjugacy class. We also show that the mapping class group of a connected orientable 2-manifold has a comeager conjugacy class if and only if the…
The author proposes a method for investigating actions of finite groups on aspherical spaces. Complete homotopy classification of free actions of finite groups on aspherical spaces is obtained. Also there are some results about non-free…
This paper describes two real analytic symplectomorphisms defined on appropriate dense open subsets of any coadjoint orbit of a compact semisimple Lie algebra. The first symplectomorphism sends the open dense subset to a bounded subset of a…
We isolate a class of groups -- called lossless groups -- for which homotopy classes of $G$-$N_\infty$ operads are in bijection with certain restricted transfer systems on the poset of conjugacy classes $\operatorname{Sub}(G)/G$.
In this paper we consider discrete groups in ${\rm PGL}_d(\mathbb{R})$ acting convex co-compactly on a properly convex domain in real projective space. For such groups, we establish necessary and sufficient conditions for the group to be…
We consider the space of countable structures with fixed underlying set in a given countable language. We show that the number of ergodic probability measures on this space that are $S_\infty$-invariant and concentrated on a single…