Related papers: The Local Rotation Set is an Interval

We consider, on a compact manifold, the group of diffeomorphisms that are isotopic to the identity. We show that every recurrent element is a distorsion element. This generalizes Avila's theorem on circle diffeomorphisms. The method also…

We show a somewhat surprising result: if $E$ is a disk in the plane $\mathbb R^2$, then there is a homeomorphism $h:\mathbb R^2\rightarrow\mathbb R^2$ such that, for every $x\in\partial E$, the orbit $O(x, h)$ is bounded, but for every…

A map on a group into itself is called a local automorphism if at any two points of the group, it can be interpolated by an automorphism of that group. In this paper we investigate the question of how local automorphisms of some classical…

There are investigated problems connected with local and boundary properties of Orlicz--Sobolev classes of finite distortion which are actively studied last time. It is showed that, a locally uniform limit of local homeomorphisms of…

In this work we study homeomorphisms of closed orientable surfaces homotopic to the identity, focusing on the existence of non-contractible periodic orbits. We show that, if $g$ is such a homeomorphism, and if $\hat g$ is its lift to the…

We apply set-valued numerical methods to compute an accurate enclosure of the rotation number. The described algorithm is supplemented with a method of proving the existence of periodic points, which is used to check the rationality of the…

We give an answer in the "geometric" setting to a question of de Fernex, Ein, and Ishii, asking when local isomorphisms of $k$-schemes can be detected on the associated maps of local arc or jet schemes. In particular, we show that their…

Let $(R,\mathfrak{m},k)$ denote a local ring. For $I$ and $J$ ideals of $R$, for all integer $i$, let $H^i_{I,J}(-)$ denote the $i$-th local cohomology functor with respect to $(I,J)$. Here we give a generalized version of Local Duality…

A rotation in a Euclidean space V is an orthogonal map on V which acts locally as a plane rotation with some fixed angle. We give a classification of all pairs of rotations in finite-dimensional Euclidean space, up to simultaneous…

We show that the connectedness of the set of parameters for which the over-rotation interval of a bimodal interval map is constant. In other words, the over-rotation interval is a monotone function of a bimodal interval map.

We introduce the notion of a point on a locally closed subset of a symplectic manifold being "locally rigid" with respect to that subset, prove that this notion is invariant under symplectic homeomorphisms, and show that coisotropic…

By a map we mean a $2$-cell decomposition of a closed compact surface, i.e., an embedding of a graph such that every face is homeomorphic to an open disc. Automorphism of a map can be thought of as a permutation of the vertices which…

A speedup, like a time change in discrete time dynamics, is a way of moving faster through the orbits of a dynamical system. Linearly recurrence is a stronger form of minimality for subshifts, shared by e.g.\ all primitive substitution…

We showed that for any bounded neighborhood of a hyperbolic equilibrium point $x_0$, there is a transformation which is locally homeomorphism, such that the system is changed into a linear system in this neighborhood. If the eigenvalues of…

We study homeomorphisms of the two-torus, homotopic to the identity, whose rotation set has non-empty interior. For such maps, we give a purely topological characterisation of elliptic islands in a chaotic sea in terms of local rotation…

After Katok, a homeomorphism $f\colon M\to M$ is said to be cohomologically $C^0$-stable when its space of real $C^0$-coboundaries is closed in $C^0(M)$. In this short note we completely classify cohomologically $C^0$-stable homeomorphisms,…

The aim of this work is to describe the set of fixed point free homeomorphisms of the plane under certain expansive conditions.

We show that every continuous rotative mapping on a closed interval has a fixed point. This gives an answer to some open questions raised by Goebel and Koter.

Let $\Delta ^{2}$ be a ball in the complex vector space $\mathbb{C}^{2}$ centered at the origin, let $f:\Delta ^{2}\to \mathbb{C}^{2}$ be a holomorphic mapping$,$ with $f(0)=0$, and let $M$ be a positive integer. If the origin 0 is an…

We study the fixed point sets of holomorphic self-maps of a bounded domain in ${\Bbb C}^n$. Specifically we investigate the least number of fixed points in general position in the domain that forces any automorphism (or endomorphism) to be…