Related papers: An spectral condition for global equivalence of pl…

Let X and Y be compact, simply connected and locally connected subsets of R^2, and let f : X -> Y be a homeomorphism isotopic to the identity on X. Generalizing Brouwer's plane translation theorem for self-maps of the plane, we prove that f…

We consider sufficient conditions which guarantee that a planar embedding has a unique fixed point. We study sufficient conditions which imply the appearing of a globally attracting fixed point for such an embedding.

In this paper, plane polynomial systems having a singular point attracting all orbits in positive time are classified up to topological equivalence. This is done by assigning a combinatorial invariant to the system (a so-called "feasible…

Let $G$ be a simple and simply connected algebraic group over an algebraically closed field $\Bbbk$ of characteristic $p>0$. Assume that $p$ is good for the root system of $G$ and that the covering map $G_{sc} \rightarrow G$ is separable.…

We show that the following conditions on a C*-algebra are equivalent: (i) it has the fixed point property for nonexpansive mappings, (ii) the spectrum of every self adjoint element is finite, (iii) it is finite dimensional. We prove that…

Using the setting of $G$-metric spaces, common fixed point theorems for four maps satisfying the weakly commuting conditions are obtained for various generalized contractive conditions. Several examples are also presented to show the…

We present a global bifurcation result for critical values of $C^1$ maps in Banach spaces. The approach is topological based on homotopy equivalence of pairs of topological spaces. For $C^2$ maps, we prove a particular global bifurcation…

We study the dynamics of planar diffeomorphisms having a unique fixed point that is a hyperbolic local saddle. We obtain sufficient conditions under which the fixed point is a global saddle. We also address the special case of…

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…

Let a>0, F: R^2 -> R^2 be a differentiable (not necessarily C^1) map and Spec(F) be the set of (complex) eigenvalues of the derivative F'(p) when p varies in R^2. (a) If Spec(F) is disjoint of the interval [1,1+a[, then Fix(F) has at most…

A parametric version of Brouwer's Fixed Point Theorem, which is proven using the fixed-point index, states that for every continuous mapping $f : (X \times Y) \to Y$, where $X$ is nonempty, compact, and connected subset of a Hausdorff…

We consider sufficient conditions to determine the global dynamics for equivariant maps of the plane with a unique fixed point which is also hyperbolic. When the map is equivariant under the action of a compact Lie group, it is possible to…

We establish the first common fixed point theorem for commutative set-valued mappings. This may help to generalize common fixed point theorems in single-valued setting to those in set-valued. We also prove the existence of a fixed point in…

We prove that if a continuous piecewise-smooth map on $\mathbb{R}^n$ is comprised of two linear functions, has a bounded orbit, and satisfies a certain non-degeneracy condition, then it has a fixed point. The result has important…

In this paper, first some results of [5] are extended for subadditive separating maps between C(X;E) and C(Y;E), such that E is a unital Banach algebra. Then we give some conditions under which a strongly subadditive map has a unique fixed…

In this paper, we study the existence of fixed points for mappings defined on complete metric space (X, d) satisfying a general contractive inequality of integral type depended on another function. This conditions is analogous of Banach…

We consider a nontrivial action of $\mathrm{C}_2$ on the type $1$ spectrum $\mathcal{Y} := \mathrm{M}_2(1) \wedge \mathrm{C}(\eta)$, which is well-known for admitting a $1$-periodic $v_1-$self-map. The resultant finite…

We consider word maps and word maps with constants on a simple algebraic group. We present results on the images of such maps, in particular, we prove a theorem on the dominance of general word maps with constants, which can be viewed as an…

In this note we define and study free global spectra: global spectra with non-trivial geometric fixed points only at the trivial group. We show that free global spectra often do not exist, and when they do, their homotopy groups satisfy…

We characterize those complete commutative positive linear ordered monoids $W$ such that whenever $f$ is a map from a Cauchy complete $W$-metric space to itself, the existence of a fixed point of $f$ is independent of the background model…