Related papers: Strong Nielsen equivalence on the punctured disc

We study relations between transitivity, mixing and periodic points on dendrites. We prove that when there is a point with dense orbit which is not an endpoint, then periodic points are dense and there is a terminal periodic decomposition…

In this article, we give two refinements of Franks' theorem: For orientation and area preserving homeomorphisms of the closed or open annulus, the existence of $k$-periodic orbits ($(k,n_0)=1$) forces the existence of infinitely many…

For a disk $D$ in the plane $\mathbb R^2$ and a plane map $f$, we give several conditions on the restriction of $f$ to the boundary $\partial D$ of $D$ which imply the existence of a fixed point of $f$ in some specified domain in $D$. These…

Kreck's modified surgery gives an approach to classifying smooth $2n$-manifolds up to stable diffeomorphism, i.e. up to connected sum with copies of $S^n \times S^n$. In dimension 4, we use a combination of modified and classical surgery to…

We give a proof of the Neilsen-Thurston classification theorem of a homeomorphism f of a standard surface of finite type as either periodic, pseudo-Anosov, or reducible. In the periodic case, we show that there exists an integer n>0 such…

Let f be an orientation-preserving homeomorphism of the plane such that f-Id is contracting. Under these hypotheses, we establish the existence, for every periodic orbit, of a fixed point which has nonzero linking number with this periodic…

We study orbits and fixed points of polynomials in a general skew polynomial ring $D[x,\sigma, \delta]$. We extend results of the first author and Vishkautsan on polynomial dynamics in $D[x]$. In particular, we show that if $a \in D$ and $f…

In this paper, we study the periodic and eventually periodic points of affine infra-nilmanifold endomorphisms. On the one hand, we give a sufficient condition for a point of the infra-nilmanifold to be (eventually) periodic. In this way we…

We prove that under the natural assumption over the dynamical degrees, the saddle periodic points of a H\'enon-like map in any dimension equidistribute with respect to the equilibrium measure. Our work is a generalization of results of…

We derive an analytical trace formula for the level density of the two-dimensional elliptic billiard using an improved stationary phase method. The result is a continuous function of the deformation parameter (eccentricity) through all…

We answer in the affirmative two conjectures made by Klein and Williams. First, in a range of dimensions, the equivariant Reidemeister trace defines a complete obstruction to removing $n$-periodic points from a self-map $f$. Second, this…

Let f be an entire function whose set of singular values is bounded and suppose that f has a Siegel disk such that f restricts to a homeomorphism of the boundary. We show that the Siegel disk is bounded. Using a result of Herman, we deduce…

We study closed, connected, spin 4-manifolds up to stabilisation by connected sums with copies of $S^2 \times S^2$. For a fixed fundamental group, there are primary, secondary and tertiary obstructions, which together with the signature…

Michael Handel has proved in [Ha] a fixed point theorem for an orientation preserving homeomorphism of the open unit disk, that turned out to be an efficient tool in the study of the dynamics of surface homeomorphisms. The present article…

We study the asymptotic behavior of the sequence of the Nielsen numbers $\{N(f^k)\}$, the essential periodic orbits of $f$ and the homotopy minimal periods of $f$ by using the Nielsen theory of maps $f$ on infra-solvmanifolds of type $R$.…

We prove some rigidity theorems for configurations of closed disks. First, fix two collections $\mathcal{C}$ and $\tilde{\mathcal{C}}$ of closed disks in the Riemann sphere $\hat{\mathbb{C}}$, sharing a contact graph which…

Any two generating systems of the fundamental group of a closed surface are Nielsen equivalent.

Given a smooth, oriented, simply-connected $4$-manifold $M$, the homological Nielsen realization problem asks: when does a finite group of isometries $G\leq O(H_2(M;\mathbb{Z}))$ preserving the intersection form lift isomorphically to a…

We use symplectic tools to establish a smooth variant of Franks theorem for a closed orientable surface of positive genus $g$; it implies that a symplectic diffeomorphism isotopic to the identity with more than $2g-2$ fixed points, counted…

Let $Y \to E \stackrel{p}{\to} B$ be a fibration and let $f: E \to E$ be a fiber map over $B$. In this work, we study the geometric and algebraic Reidemeister classes of the iterates of $f$ and introduce a Nielsen-type periodic number over…