Related papers: Flows of flowable Reeb homeomorphisms

Let $M$ be a closed and connected manifold, $H:T^*M\times \mathbb{R} / \mathbb{Z} \to \mathbb{R}$ a Tonelli $1$-periodic Hamiltonian and $\mathcal{L} \subset T^*M$ a Lagrangian submanifold Hamiltonianly isotopic to the zero section. We…

We consider AF-flows, i.e., one-parameter automorphism groups of a unital simple C*-algebra which leave invariant the dense union of an increasing sequence of finite-dimensional *-subalgebras, and derive two properties for these; an absence…

We introduce the geodesic flow on the leaves of a holomorphic foliation with leaves of dimension 1 and hyperbolic, corresponding to the unique complete metric of curvature -1 compatible with its conformal structure. We do these for the…

We define a norm on the homology of a foliated manifold, which refines and majorizes the usual Gromov norm on homology. This norm depends in an upper semi-continuous way on the underlying foliation, in the geometric topology, and can…

An orientation-preserving recurrent homeomorphism of the two-sphere which is not the identity is shown to admit exactly two fixed points. A recurrent homeomorphism of a compact surface with negative Euler characteristic is periodic.

The harmonic map energy of a map from a closed, constant-curvature surface to a closed target manifold can be seen as a functional on the space of maps and domain metrics. We consider the gradient flow for this energy. In the absence of…

We use Hamiltonian Floer theory to recover and generalize a classic rigidity theorem of Ekelend and Lasry. That theorem can be rephrased as an assertion about the existence of multiple closed Reeb orbits for certain tight contact forms on…

A homeomorphism of a compact metric space is {\em tight} provided every non-degenerate compact connected (not necessarily invariant) subset carries positive entropy. It is shown that every $C^{1+\alpha}$ diffeomorphism of a closed surface…

Let $f:M\to M$ be a dynamically coherent partially hyperbolic diffeomorphism whose center foliation has all its leaves compact. We prove that if the unstable bundle of $f$ is one-dimensional, then the volume of center leaves must be bounded…

We numerically investigate the flow structure of periodic steady water waves of fixed relative mass flux propagating on rotational flows with piece-wise constant vorticity. We show that for wave solutions along the global bifurcation…

For an open book decomposition $(S,\phi)$, the fractional Dehn twist coefficients are rational numbers measuring the amount that the monodromy $\phi$ twists the surface $S$ near each boundary component. In general, the twist coefficients do…

Planar linear flows are a one-parameter family, with the parameter $\hat{\alpha}\in [-1,1]$ being a measure of the relative magnitudes of extension and vorticity; $\hat{\alpha} = -1$, $0$ and $1$ correspond to solid-body rotation, simple…

Let $A$ be an annulus in the plane $\mathbb R^2$ and $g:A\rightarrow A$ be a boundary components preserving homeomorphism which is distal and has no periodic points. Then there is a continuous decomposition of $A$ into $g$-invariant circles…

On closed symplectically aspherical manifolds, Schwarz proved a classical result that the action function of a nontrivial Hamiltonian diffeomorphism is not constant by using Floer homology. In this article, we generalize Schwarz's theorem…

This paper is a continuation of the work in \cite{kimzhang2024} concerning Hele-Shaw flow with both drift and source terms. We prove that, in a local neighborhood, if the free boundary is Lipschitz continuous with a sufficiently small…

We consider a transversally conformal foliation $\mathcal{F}$ of a closed manifold $M$ endowed with a smooth Riemannian metric whose restriction to each leaf is negatively curved. We prove that it satisfies the following dichotomy. Either…

It is shown, for a given graph group $G$, that the fixed point subgroup Fix$\,\varphi$ is finitely generated for every endomorphism $\varphi$ of $G$ if and only if $G$ is a free product of free abelian groups. The same conditions hold for…

Let $S^*Q$ be the spherization of a closed connected manifold of dimension at least two. Consider a contactomorphism $\varphi$ that can be reached by a contact isotopy that is everywhere positively transverse to the contact structure. In…

We provide abstract conditions which imply the existence of a robustly invariant neighbourhood of a global section of a fibre bundle flow. We then apply such a result to the bundle flow generated by an Anosov flow when the fibre is the…

Interpreting RG flows as dynamical systems in the space of couplings we produce a variety of constraints, global (topological) as well as local. These constraints, in turn, rule out some of the proposed RG flows and also predict new phases…