Related papers: Properties of Fixed Point Sets and a Characterizat…

This article investigates a few questions about orbits of local automorphisms in manifolds endowed with rigid geometric structures. We give sufficient conditions for local homogeneity in a broad class of such structures, namely Cartan…

We study the dynamical properties of ball expanding maps, a class of continuous self-maps defined on compact metric spaces. For a ball expanding map, we show that: (1) the set of periodic points is dense in the chain recurrent set; (2) if…

We prove that the stable manifold of every point in a compact hyperbolic invariant set of a holomorphic automorphism of a complex manifold is biholomorphic to a complex vector space, provided that a bunching condition, which is weaker than…

It is shown, for a given graph group $G$, that the fixed point subgroup Fix$\,\varphi$ is finitely generated for every endomorphism $\varphi$ of $G$ if and only if $G$ is a free product of free abelian groups. The same conditions hold for…

We obtain an explicit parametrization of stationary discs glued to some Levi non-degenerate hypersurfaces. These discs form a family which is invariant under the action of biholomorphisms. We use this parametrization to construct a local…

The goal of this paper is to study some basic properties of the Fatou and Julia sets for a family of holomorphic endomorphisms of $\mathbb{C}^k,\; k \ge 2$. We are particularly interested in studying these sets for semigroups generated by…

Given an n-dimensional C^r-diffeomorphism g, its renormalized iteration is an iteration of g, restricted to a certain n-dimensional ball and taken in some C^r-coordinates in which the ball acquires radius 1. We show that for any r >/- 1 the…

In this paper, we are interested in the number of fixed points of functions $f:A^n\to A^n$ over a finite alphabet $A$ defined on a given signed digraph $D$. We first use techniques from network coding to derive some lower bounds on the…

We consider the covering of a ball in certain normed spaces by its congruent subsets and show that if the finite number of sets is not greater than the dimensionality of the space, then the centre of the ball either belongs to the interior…

Let G be the homeomorphism group of a dendrite. We study the normal subgroups of G. For instance, there are uncountably many non-isomorphic such groups G that are simple groups. Moreover, these groups can be chosen so that any isometric…

We study proper holomorphic maps between type-$\mathrm{I}$ irreducible bounded symmetric domains. In particular, we obtain rigidity results for such maps under certain assumptions. More precisely, let $f:D^{\mathrm{I}}_{p,q}\to…

A well-known result from Brouwer states that any orientation preserving homeomorphism of the plane with no fixed points has an empty non-wandering set. In particular, an invariant compact set implies the existence of a fixed point. In this…

We study domains in complex $n$-space with automorphism group that does not depend on the full $n$ dimensions of the ambient space. A sufficient geometric condition is obtained to guarantee that a domain has such a "thin" automorphism…

In this paper, we discuss the existence of fixed points for integral type contractions in uniform spaces endowed with both a graph and an $E$-distance. We also give two sufficient conditions under which the fixed point is unique. Our main…

We establish a fixed-point theorem for the face maps that consist in deleting the $i$th entry of an ordered set. Furthermore, we show that there exists random finite sets of integers that are almost invariant under such deletions.…

We investigate point-line geometries whose singular subspaces correspond to binary equidistant codes. The main result is a description of automorphisms of these geometries. In some important cases, automorphisms induced by non-monomial…

The Lefschetz fixed point theorem provides a powerful obstruction to the existence of minimal homeomorphisms on well-behaved spaces such as finite CW-complexes. We show that these obstructions do not hold for more general spaces. More…

In this paper, we are concerned with studying the existence of invariant complex manifolds of two-dimensional holomorphic systems. From the geometric singular perturbation theory we know that if a slow-fast system has associated a normally…

We extend a few recent results of G\'{o}rnicki (2011) asserting that the set of fixed points of an asymptotically regular mapping is a retract of its domain. In particular, we prove that in some cases the resulting retraction is H\"{o}lder…

In this article, we prove the existence of common fixed points for a pair of maps on a $q$-spherically complete $T_0$-ultra-quasi-metric space. The present article is a generalization, in the assymmetric setting of the paper of Rao et…