Related papers: Complete Conjugacy Invariants of Nonlinearizable H…

We prove a structural result for orientation-preserving actions of finitely generated solvable groups on real intervals, considered up to semi-conjugacy. As applications we obtain new answers to a problem first considered by J. F. Plante,…

Let $\text{Mod}(S_g)$ be the mapping class group of the closed orientable surface $S_g$ of genus $g\geq 2$. In this paper, we derive necessary and sufficient conditions for two finite-order mapping classes to have commuting conjugates in…

We study a simple problem that arises from the study of Lorentz surfaces and Anosov flows. For a non decreasing map of degree one $h:\mathbb{S}^1\to \mathbb{S}^1$, we are interested in groups of circle diffeomorphisms that act on the…

We consider the class of diffeomorphisms of a manifold that its differential keeps invariant a one-dimensional subbundle $E$. For that type of diffeomorphisms is naturally defined a one-parameter family called $E-$translation. We prove that…

We prove that the following three properties can not match each other on a lattice, that differentials of coordinate functions are algebraically dependent to their involutive conjugates, that the involution on a lattice is an…

Let X_o be a complex weighted-homogeneous complete intersection germ, (possibly non-reduced). Let X be a perturbation of X_o by ``higher-order-terms". We give sufficient criteria to detect fast cycles on X, via the weights of X_o. This is…

Commability is the finest equivalence relation between locally compact groups such that $G$ and $H$ are equivalent whenever there is a continuous proper homomorphism $G \to H$ with cocompact image. Answering a question of Cornulier, we show…

Subsets of a matrix algebra over a field that are invariant under conjugation and contain the linear span of each two of their commuting elements are described. They obviously include the subsets of diagonalizable and nilpotent matrices. In…

We study continuous homomorphisms between algebras of iterated Laurent series over a commutative ring. We give a full description of such homomorphisms in terms of a discrete data determined by the images of parameters. In similar terms, we…

Let f be a class P -homeomorphism of the circle. We prove that there exists a piecewise analytic homeomorphism that conjugate f to a one-class P with prescribed break points lying on pairwise distinct orbits. As a consequence, we give a…

We prove that a proper holomorphic map between two bounded symmetric domains of the same dimension, one of them being irreducible, is a biholomorphism. Our methods allow us to give a single, all-encompassing argument that unifies the…

Let $A$ be a H\"older continuous cocycle over a hyperbolic dynamical system with values in the group of diffeomorphisms of a compact manifold $M$. We consider the periodic data of $A$, i.e., the set of its return values along the periodic…

Given a result of Herman, we provide a new elementary proof of the fact that the connected component of the group of compactly supported diffeomorphisms is perfect and hence simple. Moreover, we show that every diffeomorphism $g$, which is…

The lifted horn map of a holomorphic function with a simple parabolic point is well known to be a complete local conjugacy invariant; this is a classical result proved independently by \'Ecalle, Voronin, Martinet and Ramis. Lanford and…

Let $X$ be a complex smooth quasi-projective variety with a fixed epimorphism $\nu\colon\pi_1(X)\twoheadrightarrow H$, where $H$ is a finitely generated abelian group with $\mathrm{rank}H\geq 1$. In this paper, we study the asymptotic…

We give an equivalent characterisation for the existence of a semi-conjugacy to an irrational rotation for conservative homeomorphisms of the two-torus. This leads to an analogue of Poincare's classification of circle homeomorphisms for…

Every homomorphism $\varphi: B(G) \rightarrow B(H)$ between Fourier-Stieltjes algebras on locally compact groups $G$ and $H$ is determined by a continuous mapping $\alpha: Y \rightarrow \Delta(B(G))$, where $Y$ is a set in the open coset…

A digraph is connected-homogeneous if any isomorphism between finite connected induced subdigraphs extends to an automorphism of the digraph. We consider locally-finite connected-homogeneous digraphs with more than one end. In the case that…

We prove that the complement to the caustic of a stable Lagrangian map germ of type $E_6^\pm$ has seven connected components, six of which are contractible and one is homotopy equivalent to a circle. The inverse image of the noncontractible…

Consider the holomorphic bundle with connection on $\mathbb P^1-\{0,1,\infty\}$ corresponding to the regular hypergeometric differential operator \[ \prod_{j=1}^h(D-\alpha_j)-z\prod_{j=1}^h(D-\beta_j), \qquad D=z\frac{d}{dz}. \] If the…