Related papers: Strong Nielsen equivalence on the punctured disc

Given a diffeomorphism of the plane, which has a periodic orbit, we show how Nielsen fixed point theory can be used to establish the existence of a fixed point which is linked with this periodic orbit.

This paper concerns on linked periodic orbits of orientation-preserving homeomorphisms of the $2$-disc in the sense of Gambaudo. We interpret the linking of periodic orbits by using their induced braids. Then based on the forcing relation…

We compute the generalized Lefschetz number of orientation-preserving self-homeomorphisms of a compact punctured disk, using the fact that homotopy classes of these homeomorphisms can be identified with braids. This result is applied to…

For discrete groups G, we introduce equivariant Nielsen invariants. They are equivariant analogs of the Nielsen number and give lower bounds for the number of fixed point orbits in the G-homotopy class of an equivariant endomorphism f:X->X.…

In this article we consider homeomorphisms of the open annulus $\mathbb{A}=\mathbb{R}/\mathbb{Z}\times \mathbb{R}$ which are isotopic to the identity and preserve a Borel probability measure of full support, focusing on the existence of…

In this paper, we focus our attention on the connections between the braid group and the Nielsen fixed point theory. A new forcing relation between braids is introduced, and shown that it can be fulfilled by using Nielsen fixed point…

Area and orientation preserving diffeomorphisms of the standard 2-disc, referred to as symplectomorphisms of $\mathbb{D}^{2}$, allow decompositions in terms of positive twist diffeomorphisms. Using the latter decomposition we utilize the…

We study the discrete dynamics of standard (or left) polynomials $f(x)$ over division rings $D$. We define their fixed points to be the points $\lambda \in D$ for which $f^{\circ n}(\lambda)=\lambda$ for any $n \in \mathbb{N}$, where…

The Nielsen Conjecture for Homeomorphisms asserts that any homeomorphism $f$ of a closed manifold is isotopic to a map realizing the Nielsen number of $f$, which is a lower bound for the number of fixed points among all maps homotopic to…

Let f be an orientation preserving homeomorphism of the disc D2 which possesses a periodic point of period 3. Then either f is isotopic, relative the periodic orbit, to a homeomorphism g which is conjugate to a rotation by 2 pi /3 or 4 pi…

Consider a continuous surjective self map of the open annulus with degree d > 1. It is proved that the number of Nielsen classes of periodic points is maximum possible whenever f has a completely invariant essential continuum. The same…

For the product $S_1\times S_2$ of any two connected compact hyperbolic surfaces $S_1$ and $S_2$, we give a finite bound $\mathcal{B}$ such that for any self-homeomorphism $f$ of $S_1\times S_2$ and any fixed point class $F$ of $f$, the…

Michael Handel proved in Handel (1999) the existence of a fixed point for an orientation preserving homeomorphism of the open unit disk that can be extended to the closed disk, provided that it has points whose orbits form an oriented cycle…

Let M to B, N to B be fibrations and f1,f2 :M to N be a pair of fibre-preserving maps. Using normal bordism techniques we define an invariant which is an obstruction to deforming the pair f1,f2 over B to a coincidence free pair of maps.In…

We prove a generalization of the Poincar\'e-Birkhoff theorem for the open annulus showing that if a homeomorphism satisfies a certain twist condition and the nonwandering set is connected, then there is a fixed point. Our main focus is the…

In reversible dynamical systems, it is frequently of importance to understand symmetric features. The aim of this paper is to explore symmetric periodic points of reversible maps on planar domains invariant under a reflection. We extend…

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…

M Handel has proved in [Topology 38 (1999) 235--264] a fixed point theorem for an orientation preserving homeomorphism of the open unit disk, that may be extended to the closed disk and that satisfies a linking property of orbits. We give…

For a $\mathcal{C}^1$ diffeomorphism $f:\mathbb{R}^2\rightarrow\mathbb{R}^2$ isotopic to the identity, we prove that for any value $l\in\mathbb{R}$ of the linking number at finite time of the orbits of two points there exists at least a…

We study Hamiltonian diffeomorphisms on symplectic Euclidean spaces that are equal to non-degenerate linear maps at infinity. Under the assumption that there exists an isolated homologically nontrivial fixed point satisfying the twist…