Related papers: Dynamically exotic contact spheres in dimensions $…

We classify global surfaces of section for the Reeb flow of the standard contact form on the 3-sphere, defining the Hopf fibration. As an application, we prove the degree-genus formula for complex projective curves, using an elementary…

We present new method for studying the equilibrium properties of interacting fluids in an arbitrary external filed. The method is valid in any dimension and it yields an exact results in one dimension. Using this approach, we derive a…

Given a contact structure on a closed, oriented three-manifold $Y$, we describe an invariant which takes values in the three-manifold's Floer homology $\HFa$. This invariant vanishes for overtwisted contact structures and is non-zero for…

In this paper we study the groups of contactomorphisms of a closed contact manifold from a topological viewpoint. First we construct examples of contact forms on spheres whose Reeb flow has a dense orbit. Then we show that the unitary group…

The purpose of this paper is to give a survey of the various versions of Floer homology for manifolds with contact type boundary that have so far appeared in the literature. Under the name of ``Symplectic homology'' or ``Floer homology for…

This sequel to our previous paper [MS11b] continues the study of topological contact dynamics and applications to contact dynamics and topological dynamics. We provide further evidence that the topological automorphism groups of a contact…

We consider the problem of realizing tight contact structures on closed orientable three-manifolds. By applying the theorems of Hofer et al., one may deduce tightness from dynamical properties of (Reeb) flows transverse to the contact…

We survey the interactions between foliations and contact structures in dimension three, with an emphasis on sutured manifolds and invariants of sutured contact manifolds. This paper contains two original results: the fact that a closed…

This paper associates a persistence module to a contact vector field $X$ on the ideal boundary of a Liouville manifold. The persistence module measures the dynamics of $X$ on the region $\Omega$ where $X$ is positively transverse to the…

In this paper, we show that there exists a positive density subsequence of orthonormal spherical harmonics which achieves the maximal Lp norm growth for 2<p<=6, therefore giving an example of a Riemannian surface supporting such subsequence…

We investigate certain natural connections between subriemannian geometry and hyperbolic dynamical systems. In particular, we study dynamically defined horizontal distributions which split into two integrable ones and ask: how is the energy…

Combining experimental procedures and theoretical modeling, we studied patterns, shapes, and growth of a special type of SuperAbsorbent Polymers (SAP). At the initial stage, embed in water, we have a polygonal pattern over a spherical form,…

We consider an isothermal compressible fluid evolving on a cosmological background which may be either expanding or contracting toward the future. The Euler equations governing such a flow consist of two nonlinear hyperbolic balance laws…

Let $\mathcal F$ be a co-oriented $C^2$ foliation on a closed, oriented 3-manifold. We show that $T\mathcal F$ can be perturbed to a contact structure with Reeb flow transverse to $\mathcal F$ if and only if $\mathcal F$ does not support an…

A geometric flow on $6$-dimensional symplectic manifolds is introduced which is motivated by supersymmetric compactifications of the Type IIA string. The underlying structure turns out to be SU(3) holonomy, but with respect to the projected…

We prove that in dimension 3, Anosov flows which are $\mathbb{R}$-covered and skewed are orbit equivalent to Reeb-Anosov flows. We characterize the existence of an invariant contact form or of a Birkhoff section with a given boundary, in…

On every compact, orientable, irreducible 3-manifold V which is toroidal or has torus boundary components we construct a contact 1-form whose Reeb vector field R does not have any contractible periodic orbits and is tangent to the boundary.…

We establish some new existence results for global surfaces of section of dynamically convex Reeb flows on the three-sphere. These sections often have genus, and are the result of a combination of pseudo-holomorphic curve methods with some…

In this paper we consider symplectic and contact Lie algebras. We define contactization and symplectization procedures and describe its main properties. We also give classification of such algebras in dimensions 3 and 4. The classification…

In this paper, we explore the structure of Rabinowitz--Floer homology $RFH_*$ on contact manifolds whose Reeb flow is periodic (and which satisfy an index condition such that $RFH_*$ is independent of the filling). The main result is that…