相关论文: Smooth shifts along flows

Let $(\phi_t)$ be an area-preserving smooth flow on a compact, connected, orientable surface $\mathcal M$ with at least one but finitely many fixed points. Assume that $(\phi_t)$ is analytic (up to a canonical change of coordinates) in the…

An oriented compact closed manifold is called inflexible if the set of mapping degrees ranging over all continuous self-maps is finite. Inflexible manifolds have become of importance in the theory of functorial semi-norms on homology.…

Given a closed smooth manifold $M$ of even dimension $2n\ge6$ with finite fundamental group, we show that the classifying space ${\rm BDiff}(M)$ of the diffeomorphism group of $M$ is of finite type and has finitely generated homotopy groups…

Let $M$ and $N$ be two closed $C^{\infty}$ manifolds and let $\text{Diff}_c(M)$ denote the group of $C^{\infty}$ diffeomorphisms isotopic to the identity. We prove that any (discrete) group homomorphism between $\text{Diff}_c(M)$ and…

It is a generally shared opinion that significant information about the topology of a bounded domain $\Omega $ of a riemannian manifold $M$ is encoded into the properties of the distance, $d_{\partial\Omega}$, %, $d:\Omega\rightarrow…

We establish a new criterion for the existence of a global cross section to a non-singular volume-preserving flow $\Phi$ on a closed smooth manifold $M$. Namely, if $X$ is the infinitesimal generator of the flow and $\Phi$ preserves a…

Let (M,\omega) be a compact symplectic manifold, and \phi be a symplectic diffeomorphism on M, we define a Floer-type homology FH_*(\phi) which is a gen- eralization of Floer homology for symplectic fixed points defined by Dostoglou and…

Let $G$ be a compact Lie group acting effectively by isometries on a compact Riemannian manifold $M$ with nonempty fixed point set $Fix(M,G)$. We say that the action is \emph{fixed point homogeneous} if $G$ acts transitively on a normal…

For warped products with harmonic curvature, nonconstant warping functions $\phi$, and compact two-dimensional bases $(M,h)$, we establish a dichotomy: either the Gaussian curvature $K$ of the metric $g=\phi^{-2}h$ is constant and negative,…

Let $B$ be a M\"obius band and $f:B \to \mathbb{R}$ be a Morse map taking a constant value on $\partial B$, and $\mathcal{S}(f,\partial B)$ be the group of diffeomorphisms $h$ of $B$ fixed on $\partial B$ and preserving $f$ in the sense…

Let $G$ be a topological group, let $\phi$ be a continuous endomorphism of $G$ and let $H$ be a closed $\phi$-invariant subgroup of $G$. We study whether the topological entropy is an additive invariant, that is,…

We consider the dependence on parameters of the solutions of cohomology equations over Anosov diffeomorphisms. We show that the solutions depend on parameters as smoothly as the data. As a consequence we prove optimal regularity results for…

In this article we consider the general problem of translating definitions and results from the category of discrete-time dynamical systems to the category of flows. We consider the dynamics of homeomorphisms and flows on compact metric…

We show that if $E \i \R^n$ is a Reifenberg flat set $E$ of dimension $d$ at scale $r_0$, we can find a smooth surface $\Sigma_0$ of dimension $d$ which is close to $E$ at the scale $r_0$. When $E$ is a Reifenberg flat set, this allows us…

Let $M$ be a compact manifold equipped with a pair of complementary foliations, say horizontal and vertical. In Catuogno, Silva and Ruffino ($Stoch$. $Dyn$., 2013) it is shown that, up to a stopping time $\tau$, a stochastic flow of local…

In this work we study the problem of positiveness of topological entropy for flows using pointwise dynamics. We show that the existence of a non-periodic nonwandering point of an expansive and non-singular flow with shadowing is a…

Hamiltonian flows on compact surfaces are characterized, and the topological invariants of such flows with finitely many singular points are constructed from the viewpoints of integrable systems, fluid mechanics, and dynamical systems.…

In this paper, we classify compact simply connected cohomogeneity one manifolds up to equivariant diffeomorphism whose isotropy representation by the connected component of the principal isotropy subgroup has three or less irreducible…

A point-shift $F$ maps each point of a point process $\Phi$ to some point of $\Phi$. For all translation invariant point-shifts $F$, the $F$-foliation of $\Phi$ is a partition of the support of $\Phi$ which is the discrete analogue of the…

We consider volume-preserving flows $(\Phi^f_t)_{t\in\mathbb{R}}$ on $S\times \mathbb{R}$, where $S$ is a closed connected surface of genus $g\geq 2$ and $(\Phi^f_t)_{t\in\mathbb{R}}$ has the form $\Phi^f_t(x,y)=(\phi_tx,y+\int_0^t…