Related papers: Distortion for diffeomorphisms of surfaces with bo…

We characterize finite sets $S$ of nonwandering points for generic diffeomorphisms $f$ as those which are {\em uniformly bounded}, i.e., there is an uniform bound for small perturbations of the derivative of $f$ along the points in $S$ up…

Suppose f is a C^{1+\epsilon} surface diffeomorphism with positive topological entropy. For every positive \delta strictly smaller than the topological entropy of f we construct an invariant Borel set E such that (a) f|E has a countable…

Suppose G is an almost simple group containing a subgroup isomorphic to the three-dimensional integer Heisenberg group. For example any finite index subgroup of SL(3,Z) is such a group. The main result of this paper is that every action of…

Let $f $ be a Morse function on a smooth compact surface $M$ and $\mathcal{S}'(f)$ be a group of $f$-preserving diffeomorphisms of $M$ which are isotopic to the identity map. Let also $G(f)$ be a group of automorphisms of the graph of $f$…

In this article, we study the smooth mapping class group of a surface S relative to a given Cantor set, that is the group of isotopy classes of orientation-preserving smooth diffeomorphisms of S which preserve this Cantor set. When the…

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…

We consider a class $G(S^n)$ of orientation preserving Morse-Smale diffeomorphisms of the sphere $S^{n}$ of dimension $n>3$ in assumption that invariant manifolds of different saddle periodic points have no intersection. We put in a…

In this paper we consider closed orientable surfaces $S$ of positive genus and $C^r$-diffeomorphisms $f:S\rightarrow S$ isotopic to the identity ($r\geq 1)$. The main objective is to study periodic open topological disks which are…

Given a compact surface $M$, consider the natural right action of the group of diffeomorphisms $\mathcal{D}(M)$ of $M$ on $\mathcal{C}^{\infty}(M,\mathbb{R})$ defined by the rule: $(f,h)\mapsto f\circ h$ for $f\in…

The first main result is a topological rigidity theorem for complete immersed hypersurfaces of spherical space forms which extends similar results due to do Carmo/Warner, Wang/Xia and Longa/Ripoll. Under certain sharp conditions on the…

A diffeomorphism f is called super exponential divergent if for every r>1, the lower limit of #Per_n(f)/r^n diverges to infinity as n tends to infinity, where Per_n(f) is the set of all periodic points of f with period n. This property is…

The $\pi_2$-diffeomorphism finiteness result (\cite{FR1,2}, \cite{PT}) asserts that the diffeomorphic types of compact $n$-manifolds $M$ with vanishing first and second homotopy groups can be bounded above in terms of $n$, and upper bounds…

Let S be a closed surface with nonzero Euler characteristic. We prove the existence of an open neighborhood V of the identity map of S in the C^1-topology with the following property: if G is an abelian subgroup of Diff^1(S) generated by…

For an arbitrary convex function $\Psi:[1,\infty) \to [1,\infty)$, we consider uniqueness in the following two related extremal problems: Problem A boundary value problem: Establish the existence of, and describe the mapping $f$, achieving…

In this paper we discuss the relationship between groups of diffeomorphisms of spheres and balls. We survey results of a topological nature and then address the relationship as abstract (discrete) groups. We prove that the identity…

We show that generically a pseudogroup generated by holomorphic diffeomorphisms defined about $0 \in \mathbb{C}$ is free in the sense of pseudogroups even if the class of conjugacy of the generators is fixed. This result has a number of…

In this paper, we prove that each automorphism of the Torelli group of a surface is induced by a diffeomorphism of the surface, provided that the surface is a closed, connected, orientable surface of genus at least 3. This result was…

We show that the identity component of the group of diffeomorphisms of a closed oriented surface of positive genus admits many unbounded quasi-morphisms. As a corollary, we also deduce that this group is not uniformly perfect and its…

Let $f:M\to \mathbb{R}$ be a Morse function on a smooth closed surface, $V$ be a connected component of some critical level of $f$, and $\mathcal{E}_V$ be its atom. Let also $\mathcal{S}(f)$ be a stabilizer of the function $f$ under the…

For a compact smooth manifold $M$ (with boundary) we prove that the topological rank of the diffeomorphism group Diff$_0^k(M)$ is finite for all $k\geq 1$. This extends a result from [2] where the same claim is proved in the special case of…