Related papers: Pointwise rotation for homeomorphisms with integra…

A primary goal in this paper is to study the question that asks when a real analytic submanifold $M$ in ${\mathbb{C}}^{n+1}$ bounds a real analytic (up to $M$) Levi-flat hypersurface $\hat{M}$ near $p\in M$ such that $\hat{M}$ is foliated…

For an arbitrary convex function $\Psi:[1,\infty) \to [1,\infty)$, we consider uniqueness in the following two related extremal problems: Problem A boundary value problem: Establish the existence of, and describe the mapping $f$, achieving…

Let $f:\Omega\to\IR^2$ be a mapping of finite distortion, where $\Omega\subset\IR^2 .$ Assume that the distortion function $K(x,f)$ satisfies $e^{K(\cdot, f)}\in L^p_{loc}(\Omega)$ for some $p>0.$ We establish optimal regularity and area…

We prove the strong $C^\infty$ closing property, as formulated by Irie, for a class of Hamiltonian diffeomorphisms which includes all pseudo-rotations of projective spaces as well as all Anosov-Katok pseudo-rotations.

We analyze the inverse problem of recovering geometric information from the return map induced by a round-trip between a convex core C and an admissible domain. This process defines a discrete dynamical system on the boundary of C governed…

A well-known result from Brouwer states that any orientation preserving homeomorphism of the plane with no fixed points has an empty non-wandering set. In particular, an invariant compact set implies the existence of a fixed point. In this…

The goals of this paper are to obtain theoretical models of what happens when a computer calculates the rotation set of a homeomorphism, and to find a good algorithm to perform simulations of this rotation set. To do that we introduce the…

We deal with germs of diffeomorphisms that are reversible under an involution. We establish that this condition implies that, in general, both the family of reversing symmetries and the group of symmetries are not finite, in contrast with…

We study a second order ordinary differential equation corresponding to rotationally symmetric $p$-harmonic maps. We show unique continuation and Liouville's type theorems for positive solutions. We discuss the existence of bounded positive…

Consider Yudovich solutions to the incompressible Euler equations with bounded initial vorticity in bounded planar domains or in $\mathbb{R}^2$. We present a purely Lagrangian proof that the solution map is strongly continuous in $L^p$ for…

The rigidity theory for circle homeomophisms with breaks was studied intensively in the last 20 years. It was proved that under mild conditions of the Diophantine type on the rotation number any two $C^{2+\alpha}$ smooth circle…

This paper is a first of a series of three papers which study eta invariants for laminations. In this first paper, we extend the results of Higson and Roe to deal with regular (unbounded) operators and more importantly to take into account…

Let $\mathbb{A}$ be an annulus in the plane $\mathbb R^2$ and $g:\mathbb{A}\rightarrow \mathbb{A}$ be a boundary components preserving homeomorphism which is distal and has no periodic points. In \cite{SXY}, the authors show that there is a…

We construct a family of rotating vortex patches with fixed angular velocity for the two-dimensional Euler equations in a disk. As the vorticity strength goes to infinity, the limit of these rotating vortex patches is a rotating point…

In this paper we provide extensions of the $\lambda$-Lemma (also known as Inclination Lemma) for piecewise smooth vector fields and maps. In order to achieve our main result, we investigate the regularity of time-T-maps of piecewise smooth…

We determine the homeomorphism type of the space of smooth complete nonnegatively curved metrics on surfaces of positive Euler characteristic equipped with the topology of $C^\gamma$ uniform convergence on compact sets, when $\gamma$ is…

We prove a generalization of the fixed point theorem of Cartwright and Littlewood. Namely, suppose $h : \mathbb{R}^2 \to\mathbb{R}^2$ is an orientation preserving planar homeomorphism, and let $C$ be a continuum such that $h^{-1}(C)\cup C$…

We determine the bounded cohomology of the group of homeomorphisms of certain low-dimensional manifolds. In particular, for the group of orientation-preserving homeomorphisms of the circle and of the closed 2-disc, it is isomorphic to the…

Let $f$ be an orientation and area preserving diffeomorphism of an oriented surface $M$ with an isolated degenerate fixed point $z_0$ with Lefschetz index one. Le Roux conjectured that $z_0$ is accumulated by periodic orbits. In this…

We characterize two classical types of conformality of a holomorphic self-map of the unit disk at a boundary point - existence of a finite angular derivative in the sense of Carath\'eodory and the weaker property of angle preservation - in…