Related papers: $R$-closed homeomorphisms on surfaces

Let S be a compact connected surface and let f be an element of the group Homeo\_0(S) of homeomorphisms of S isotopic to the identity. Denote by \tilde{f} a lift of f to the universal cover of S. Fix a fundamental domain D of this universal…

The aim of this note is to stablish the topological classification of finite period orientation reversing autohomeomorphims of a closed oriented surface when the period is 2q, with q even. The classification of periodic orientation…

Gradient-like diffeomorphisms of a closed surface $M^2$ are characterized by a finite hyperbolic limit set and the absence of intersections of invariant manifolds of distinct saddle points. In the case where such diffeomorphisms $f_0,…

We show a somewhat surprising result: if $E$ is a disk in the plane $\mathbb R^2$, then there is a homeomorphism $h:\mathbb R^2\rightarrow\mathbb R^2$ such that, for every $x\in\partial E$, the orbit $O(x, h)$ is bounded, but for every…

We prove the existence of at least $cl(M)$ periodic orbits for certain time dependant Hamiltonian systems on the cotangent bundle of an arbitrary compact manifold $M$. These Hamiltonians are not necessarily convex but they satisfy a certain…

Consider a domain D in R^3 which is convex (possibly all R^3) or which is smooth and bounded. Given any open surface M, we prove that there exists a complete, proper minimal immersion f : M --> D. Moreover, if D is smooth and bounded, then…

A method is suggested for construction of quadrangulations of the closed orientable surface with given genus g and either (1) with given chromatic number or (2) with given order allowed by the genus g. In particular, N. Hartsfield and G.…

Given a real closed field $R$, we identify exactly four proper reducts of $R$ which expand the underlying (unordered) $R$-vector space structure. Towards this theorem we introduce a new notion, of strongly bounded reducts of linearly…

We prove a "gluing" theorem for monotone homotopies; a monotone homotopy is a homotopy through simple contractible closed curves which themselves are pairwise disjoint. We show that two monotone homotopies which have appropriate overlap can…

This paper studies homeomorphisms of the closed annulus that are isotopic to the identity from the viewpoint of rotation theory, using a newly developed forcing theory for surface homeomorphisms. Our first result is a solution to the so…

Let $X$ be a compact metric space and let $f:X\rightarrow X$ be a homeomorphism on $X$. We show that if $f$ is both pointwise recurrent and expansive, then the dynamical system $(X, f)$ is topologically conjugate to a subshift of some…

We prove that for every nonnegative integer $g$, there exists a bound on the number of ends of a complete, embedded minimal surface $M$ in $\mathbb{R}^3$ of genus $g$ and finite topology. This bound on the finite number of ends when $M$ has…

We give a combinatorial characterization of the group of quasiconformal homeomorphisms of a closed, oriented surface $S$ of genus at least $2$. In particular, we prove they are exactly the automorphisms of a graph of essential quasicircles…

In this paper, we consider complete non-catenoidal minimal surfaces of finite total curvature with two ends. A family of such minimal surfaces with least total absolute curvature is given. Moreover, we obtain a uniqueness theorem for this…

We study the rotational behaviour on minimal sets of torus homeomorphisms and show that the associated rotation sets can be any type of line segments as well as non-convex and even plane-separating continua. This shows that restrictions…

The Lefschetz fixed point theorem provides a powerful obstruction to the existence of minimal homeomorphisms on well-behaved spaces such as finite CW-complexes. We show that these obstructions do not hold for more general spaces. More…

We prove several generic existence results for infinitely many periodic orbits of Hamiltonian diffeomorphisms or Reeb flows. For instance, we show that a Hamiltonian diffeomorphism of a complex projective space or Grassmannian generically…

Given a finite set $E$, a subset $D\sub E$ (viewed as a function $E\to \F_2$) is orthogonal to a given subspace $\FF$ of the $\F_2$-vector space of functions $E\to \F_2$ as soon as $D$ is orthogonal to every $\sub$-minimal element of $\FF$.…

For Finsler metrics (no reversibility assumed) on closed orientable surfaces of genus greater than one, we study the dynamics of minimal rays and minimal geodesics in the universal cover. We prove in particular, that for almost all…

We construct families of embedded, singly periodic minimal surfaces of any genus $g$ in the quotient with any even number $2n>2$ of almost parallel Scherk ends. A surface in such a family looks like $n$ parallel planes connected by $n-1+g$…