Related papers: A fixed point theorem for plane homeomorphisms wit…
We study groups of homeomorphisms of R, each of whose elements have at most one fixed point. In particular we prove that any such group of C^2 diffeomorphisms is topologically conjugate to an affine group.
We define the infinite dimensional simplex to be the closure of the convex hull of the standard basis vectors in R^infinity, and prove that this space has the 'fixed point property': any continuous function from the space into itself has a…
We establish a purely geometric form of the concentration theorem (also called localization theorem) for actions of a linearly reductive group $G$ on an affine scheme $X$ over an affine base scheme $S$. It asserts the existence of a…
This is an expository paper giving a proof of the existence and uniqueness of smooth structures (hence also PL structures) on topological surfaces. Most published proofs rely on the topological Schoenflies theorem, but here we use instead…
We investigate fixed point properties for isometric actions of topological groups on a wide class of metric spaces, with a particular emphasis on Hilbert spaces. Instead of requiring the action to be continuous, we assume that it is…
We demonstrate that there is a large class of compact metric spaces for which the shadowing property can be characterized as a structural property of the space of dynamical systems. We also demonstrate for this class of spaces, that in…
In the vector-field guided path-following problem, a sufficiently smooth vector field is designed such that its integral curves converge to and move along a one-dimensional geometric desired path. The existence of singular points where the…
We prove a structure theorem for ergodic homological rotation sets of homeomorphisms isotopic to the identity on a closed orientable hyperbolic surface: this set is made of a finite number of pieces that are either one-dimensional or almost…
A space X has the local fixed point property LFPP, (local periodic point property LPPP) if it has an open basis $\mathcal{B}$ such that, for each $B\in \mathcal{B}$, the closure $\overline{B}$ has the fixed (periodic) point property. Weaker…
This paper is devoted to studying of some properties of multivalued mappings in Euclidean space. There were proved theorems on a fixed point for multivalued mappings whose restrictions to some subset in the closure of a domain satisfy "a…
In this paper, we investigate the existence of fixed-point-free automorphisms for finite-dimensional Lie algebras. By a result of Jacobson, a Lie algebra admitting a fixed-point-free automorphism is solvable. We prove that such a Lie…
The topological Tverberg theorem states that any continuous map of a $(d+1)(r-1)$-simplex into the Euclidean $d$-space maps some points from $r$ pairwise disjoint faces of the simplex to the same point whenever $r$ is a prime power. We…
Well-founded fixed points have been used in several areas of knowledge representation and reasoning and to give semantics to logic programs involving negation. They are an important ingredient of approximation fixed point theory. We study…
We study some topological properties of attractors.
This paper studies topological definitions of chain recurrence and shadowing for continuous endomorphisms of topological groups generalizing the relevant concepts for metric spaces. It is proved that in this case the sets of chain recurrent…
A path-following control algorithm enables a system's trajectories under its guidance to converge to and evolve along a given geometric desired path. There exist various such algorithms, but many of them can only guarantee local convergence…
We prove that every factor map between topological flows preserves the standard shadowing property if it is injective except for a closed orbit that shrinks to a singularity. As an application, we construct a $C^\infty$-flow on a…
The present paper aims at representing an improvement of the result in [2], where a strong unique continuation property and a description of the local behaviour around the edge of a crack for solutions to an elliptic problem are…
We study fixed point sets for holomorphic automorphisms (and endomorphisms) on complex manifolds. The main object of our interest is to determine the number and configuration of fixed points that forces an automorphism (endomorphism) to be…
This work is a comparative study between the existence of fixed point for homomorphisms in a class of binary relationnal systems and the existence of fixed point for nonexpansive mappings in semimetric spaces.