Related papers: Centralizer of fixed point free separating flows

Let $\T$ be a $2$-torsion free triangular ring and let $\varphi:\T\rightarrow \T$ be an additive map. We prove that if $\A \varphi(\B)+\varphi(\B)\A=0$ whenever $\A,\B\in \T$ are such that $\A\B=\B\A=0$, then $\varphi$ is a centralizer. It…

Self-similar stable mixed moving average processes can be related to nonsingular flows through their minimal representations. Self-similar stable mixed moving averages related to dissipative flows have been studied, as well as processes…

This is a continuation of the research in [16]. Let $(\overline{M},g_{-1})$ be a closed geodesic $r_0$-ball in the hyperbolic space $(\mathbb{H}^n,g_{-1})$. Let $m\neq1$ be a positive constant. In this paper, we show that for $n\geq3$,…

To every dynamical system $(X,\varphi)$ over a totally disconnected compact space, we associate a left-orderable group $T(\varphi)$. It is defined as a group of homeomorphisms of the suspension of $(X,\varphi)$ which preserve every orbit of…

Hamiltonian dynamical systems tend to have infinitely many periodic orbits. For example, for a broad class of symplectic manifolds almost all levels of a proper smooth Hamiltonian carry periodic orbits. The Hamiltonian Seifert conjecture is…

Let $\Phi$ be a flow on a smooth, compact, finite-dimensional manifold $M$. Consider the subsets $E(\Phi)$ and $D(\Phi)$ of $C^{\infty}(M,M)$ consisting of smoothh mappings and diffeomorphisms (respectively) of $M$ preserving the foliation…

We obtain a exponential large deviation upper bound for continuous observables on suspension semiflows over a non-uniformly expanding base transformation with non-flat singularities or criticalities, where the roof function defining the…

We discover a rigidity phenomenon within the volume-preserving partially hyperbolic diffeomorphisms with $1$-dimensional center. In particular, for smooth, ergodic perturbations of certain algebraic systems -- including the discretized…

We study the $L^2$-gradient flows, $\partial_t u-\mathrm{div}(\mathrm{D}f(x,\mathbb{A}u))=0$, of functionals of the type $\int_{\Omega}f(x,\mathbb{A}u)\,\mathrm{d}x$, where $f$ is a convex function of linear growth and $\mathbb{A}$ is some…

In this paper, we set up a new Yamabe type flow on a compact Riemannian manifold $(M,g)$ of dimension $n\geq 3$. Let $\psi(x)$ be any smooth function on $M$. Let $p=\frac{n+2}{n-2}$ and $c_n=\frac{4(n-1)}{n-2}$. We study the Yamabe-type…

Let $\Omega$ be a compact Riemannian manifold with smooth boundary and let $u_t$ be the solution of the heat equation on $\Omega$, having constant unit initial data $u_0=1$ and Dirichlet boundary conditions ($u_t=0$ on the boundary, at all…

For any flag manifold $M=G/K$ of a compact simple Lie group $G$ we describe non-collapsing ancient invariant solutions of the homogeneous unnormalized Ricci flow. Such solutions emerge from an invariant Einstein metric on $M$, and by…

For an orientation-preserving homeomorphism of the sphere, we prove that if a translation line does not accumulate in a fixed point, then it necessarily spirals towards a topological attractor. This is in analogy with the description of…

The fixed points of the generalized Ricci flow are the Bismut Ricci flat metrics, i.e., a generalized metric $(g,H)$ on a manifold $M$, where $g$ is a Riemannian metric and $H$ a closed $3$-form, such that $H$ is $g$-harmonic and…

We prove that if $f:I\subset \Bbb R\to \Bbb R$ is of bounded variation, then the noncentered maximal function $Mf$ is absolutely continuous, and its derivative satisfies the sharp inequality $\|DMf\|_1\le |Df|(I)$. This allows us obtain,…

There is an extensive and growing body of work analyzing convex ancient solutions to Mean Curvature Flow (MCF), or equivalently of Rescaled Mean Curvature Flow (RMCF). The goal of this paper is to complement the existing literature, which…

We present a symmetry result regarding stationary solutions of the 2D Euler equations in a disk. We prove that in a disk, a steady flow with only one stagnation point and tangential boundary conditions is a circular flow, which confirms a…

We consider a counting problem in the setting of hyperbolic dynamics. Let $\phi_t : \Lambda \to \Lambda$ be a weak mixing hyperbolic flow. We count the proportion of prime periodic orbits of $\phi_t$, with length less than $T$, that satisfy…

In this paper, we study the regularized mean curvature flow starting from invariant hypersurfaces in a Hilbert space equipped with an isometric almost free Hilbert Lie group action whose orbits are minimal regularizable submanifolds, where…

The main result of this paper shows that, if $g(t)$ is a complete non-singular solution of the normalized Ricci flow on a noncompact 4-manifold $M$ of finite volume, then the Euler characteristic number $\chi(M)\geq0$. Moreover,…