Related papers: Groups of volume-preserving diffeomorphisms of non…

Link invariants of long pieces of orbits of a volume-preserving flow can be used to define diffeomorphism invariants of the flow. In this paper, we extend the notions of wrapping number and trunk and define invariants of links with respect…

We give a classification of generic coadjoint orbits for the group of area-preserving diffeomorphisms of a closed non-orientable surface. This completes V. Arnold's program of studying invariants of incompressible fluids in 2D. As an…

We prove the following result: Let $(M,g_0)$ be a compact manifold of dimension $n\geq 12$ with positive isotropic curvature. Then $M$ is diffeomorphic to a spherical space form, or the total space of an orbifiber bundle over $\mathbb{S}^1$…

We show the existence of a weak bi-invariant symmetric nondegenerate 2-form on the contact diffeomorphisms group $\mathcal{D}_\theta$ of a contact Riemannian manifold $(M,g,\theta)$ and study its properties. We describe the Euler's equation…

We study a special kind of singular vorticities in ideal 2D fluids that combine features of point vortices and vortex sheets, namely pointed vortex loops. We focus on the coadjoint orbits of the area-preserving diffeomorphism group of…

Denote by $\DC(M)_0$ the identity component of the group of the compactly supported $C^r$ diffeomorphisms of a connected $C^\infty$ manifold $M$. We show that if $\dim(M)\geq2$ and $r\neq \dim(M)+1$, then any homomorphism from $\DC(M)_0$ to…

In this paper we study boundedness of conjugation invariant norms on diffeomorphism groups of manifold pairs. For the diffeomorphism group ${\mathcal D} \equiv {\rm Diff}(M,N)_0$ of a closed manifold pair $(M, N)$ with $\dim N \geq 1$,…

We study the approximate controllability problem for Liouville transport equations along a mechanical Hamiltonian vector field. Such PDEs evolve inside the orbit $$\mathcal{O}(\rho_0):=\left\{\rho_0\circ \Phi\mid \Phi\in {\rm…

We study groups of circle diffeomorphisms whose action on the cylinder $\mathcal C=\mathbb S^1\times \mathbb S^1\setminus \Delta$ preserves a volume form. We first show that such a group is topologically conjugate to a subgroup of…

Using techniques from TRO equivalence of masa bimodules we prove various transference results: We show that when $\alpha$ is a group homomorphism which pushes forward the Haar measure of $G$ to a measure absolutely continuous with respect…

Diffeomorphism groups $G$ of manifolds $M$ on locally $\bf F$-convex spaces over non-Archimedean fields $\bf F$ are investigated. It is shown that their structure has many differences with the diffeomorphism groups of real and complex…

We discuss various infinite-dimensional configuration spaces that carry measures quasiinvariant under compactly-supported diffeomorphisms of a manifold M corresponding to a physical space. Such measures allow the construction of unitary…

We discuss two distinct realizations of the diffeomorphism group for metric gravity, which give rise to theories that are classically equivalent, but quantum mechanically distinct. We renormalize them in $d=2+\epsilon$ dimensions,…

Following the recent advances in the study of groups of circle diffeomorphisms, we describe an efficient way of classifying the topological dynamics of locally discrete, finitely generated, virtually free subgroups of the group…

In this paper, we define and study strong right-invariant sub-Riemannian structures on the group of diffeomorphisms of a manifold with bounded geometry. We derive the Hamiltonian geodesic equations for such structures, and we provide…

Let $D$ be a 2-dimensional closed unit disk and $\rm{Symp}(D,0)_{\rm{rel}}$ the group of symplectomorphisms preserving the origin and the boundary $\partial D$ pointwise. We consider the $\mathbb{R}$-valued flux homomorphism on…

We prove that the group of contact diffeomorphisms is closed in the group of all diffeomorphisms in the C^0-topology. By Gromov's alternative, it suffices to exhibit a diffeomorphism that can not be approximated uniformly by contact…

Let $M$ be an oriented smooth manifold, and $\operatorname{Homeo}(M,\omega)$ the group of measure preserving homeomorphisms of $M$, where $\omega$ is a finite measure induced by a volume form. In this paper we define volume and Euler…

We prove a C^1-connecting lemma for pseudo-orbits of diffeomorphisms on compact manifolds. We explore some consequences for C^1-generic diffeomorphisms. For instance, C^1-generic conservative diffeomorphisms are transitive. <br> Nous…

Asaoka & Irie recently proved a $C^{\infty}$ closing lemma of Hamiltonian diffeomorphisms of closed surfaces. We reformulated their techniques into a more general perturbation lemma for area-preserving diffeomorphism and proved a…