Related papers: Flowability of plane homeomorphisms

Unconfined granular flows along an inclined plane are investigated experimentally. During a long transient, the flow gets confined by quasistatic banks but still spreads laterally towards a well-defined asymptotic state following a…

We give a criterion when a planar tree-like curve, i.e. a generic immersed plane curve each double point of which cuts it into two disjoint parts, can be send by a diffeomorphism of the plane onto a curve with no inflection points. We also…

In this paper, we define the recurrence and "non-wandering" for decompositions. The following inclusion relations hold for codimension one foliations on closed $3$-manifolds: $\{$minimal$\} \sqcup \{$compact$\}$ $\subsetneq$ $\{$pointwise…

The notion of S-stability of foliations on branched simple polyhedrons is introduced by R. Benedetti and C. Petronio in the study of characteristic foliations of contact structures on 3-manifolds. We additionally assume that the 1-form…

We consider a self-homeomorphism h of some surface S. A subset F of the fixed point set of h is said to be unlinked if there is an isotopy from the identity to h that fixes every point of F. With Le Calvez' transverse foliations theory in…

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…

Adapting the construction of global Kuranishi charts to the contact setting, we associate to any non-degenerate contact manifold a flow category based on Reeb orbits and moduli spaces of pseudo-holomorphic buildings. The construction lifts…

Let $M$ be a smooth ($C^{\infty}$) manifold, $F_1,...,F_n$ be vector fields on $M$ generating the corresponding flows $\Phi_1,...,\Phi_n$, and $\alpha_1,...,\alpha_{n}:M\to \mathbb{R}$ smooth functions. Define the following map $f:M\to M$…

It is shown that if a non-invertible area preserving local homeomorphism on $\mathbb{T}^2$ is homotopic to a linear expanding or hyperbolic endomorphism, then it must be topologically transitive. This gives a complete characterization, in…

Let $h : \mathbb{R}^2 \to \mathbb{R}^2$ be an orientation preserving homeomorphism of the plane. For any bounded orbit $\mathcal{O}(x)=\{h^n(x):n\in\mathbb{Z}\}$ there exists a fixed point $x'\in\mathbb{R}^2$ of $h$ linked to…

An area-preserving homeomorphism isotopic to the identity is said to have rational rotation direction if its rotation vector is a real multiple of a rational class. We give a short proof that any area-preserving homeomorphism of a compact…

We prove that any planar birational integrable map, which preserves a fibration given by genus $0$ curves has a Lie symmetry and some associated invariant measures. The obtained results allow to study in a systematic way the global dynamics…

We show that the Gromov-Hausdorff limit of a sequence of leaves in a compact foliation is a covering space of the limiting leaf which is no larger than this leaf's holonomy cover. We also show that convergence to such a limit is smooth…

In this paper we prove the stochastic homeomorphism flow property and the strong Feller property for stochastic differential equations with sigular time dependent drifts and Sobolev diffusion coefficients. Moreover, the local well posedness…

Helicity is a fundamental conserved quantity in physical systems governed by vector fields whose evolution is described by volume-preserving transformations on a three-manifold. Notable examples include inviscid, incompressible fluid flows,…

We study the geometric flow of a planar curve driven by its curvature and the normal derivative of its capacity potential. Under a convexity condition that is natural to our problem, we establish long term existence and large time…

For any Riemannian foliation F on a closed manifold M with an arbitrary bundle-like metric, leafwise heat flow of differential forms is proved to preserve smoothness on M at infinite time. This result and its proof have consequences about…

Plane Couette flow presents a regular oblique turbulent-laminar pattern over a wide range of Reynolds numbers R between the globally stable base flow profile at low R<R_g and a uniformly turbulent regime at sufficiently large R>R_t. The…

We prove that a Morse-Smale gradient-like flow on a closed manifold has a "system of compatible invariant stable foliations" that is analogous to the object introduced by Palis and Smale in their proof of the structural stability of…

In this work, we study a gap phenomenon in locally conformally flat Riemannian manifolds with non-negative Ricci curvature. We construct complete solutions to the Yamabe flow that exhibit instantaneous bounded curvature as they evolve.…