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Let G be a group acting on the plane by orientation-preserving homeomorphisms. We show that if for some k>0 there is a ball of radius r > k/\sqrt{3} such that each point x in the ball satisfies |gx -hx| < k for all g, h in G, and the action…

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…

In this paper we study the existence and uniqueness of fixed points of a class of mappings defined on complete, (sequentially compact) cone metric spaces, without continuity conditions and depending on another function.

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…

A general fixed point theorem for isometries in terms of metric functionals is proved under the assumption of the existence of a conical bicombing. It is new even for isometries of Banach spaces as well as for non-locally compact…

For every $r\in\mathbb{N}_{\geq 2}\cup\{\infty\}$, we prove a $C^r$-orbit connecting lemma for dynamically coherent and plaque expansive partially hyperbolic diffeomorphisms with 1-dimensional orientation preserving center bundle. To be…

We prove that if the stable foliation and the unstable foliation of an Anosov diffeomorphism on a connected compact manifold are $C^3$, then the diffeomorphism has fixed points. This is a partial positive answer to a Smale conjecture for…

A trajectory isomorphism between the two Newtonian fixed center problem in the sphere and two associated planar two fixed center problems is constructed by performing two simultaneous gnomonic projections in $S^2$. This isomorphism converts…

The relation between fixed point and orbit count sequences is investigated from the point of view of linear mappings on the space of arithmetic functions. Spectral and asymptotic properties are derived and several quantities are explicitly…

We present an algorithm for constructing the fixed point of a general non-isometric similarity of the plane.

In this paper we prove some new fixed point theorems for multivalued mappings on orbitally complete uniform spaces.

We study main bifurcations of multidimensional diffeomorphisms having a non-transversal homoclinic orbit to a saddle-node fixed point. On a parameter plane we build a bifurcation diagram for single-round periodic orbits lying entirely in a…

We characterize the sequences of fixed point indices $\{i(f^n, p)\}_{n\ge 1}$ of fixed points that are isolated as an invariant set and continuous maps in the plane. In particular, we prove that the sequence is periodic and $i(f^n, p) \le…

We face the problem of characterizing the periodic cases in parametric families of (real or complex) rational diffeomorphisms having a fixed point. Our approach relies on the Normal Form Theory, to obtain necessary conditions for the…

We present new criteria on the existence of fixed points that combine some monotonicity assumptions with the classical fixed point index theory. As an illustrative application, we use our theoretical results to prove the existence of…

The Lefschetz fixed point theorem and its converse have many generalizations. One of these generalizations is to endomorphisms of a space relative to a fixed subspace. In this paper we define relative Lefschetz numbers and Reidemeister…

These largely expository notes describe the properties of the function ${\cal R}$ which assigns a number to a $4$-tuple of distinct fixed points of an orientation preserving homeomorphism or diffeomorphism of $S^2$.

We prove three theorems giving fixed points for orientation preserving homeomorphisms of the plane following forgotten results of Brouwer.

We give a new proof of Cartan's fixed point theorem using topological fixed point theory. For an odd dimensional, simply connected and complete manifold having non-positive curvature, we further prove that every isometry with finite order…

In this paper, we establish some fixed point theorems in ordered partial metric spaces. An example is given to illustrate our obtained results.