Related papers: Zero Entropy Interval Maps And MMLS-MMA Property

We obtain that Sarnak's M\"{o}bius Disjointness Conjecture holds for product flows between affine linear flows on compact abelian groups of zero topological entropy and a class of rigid dynamical systems. To prove this, we show an estimate…

We study the topological entropy of the magnetic flow on a closed riemannian surface. We prove that if the magnetic flow has a non-hyperbolic closed orbit in some energy set T^cM= E^{-1}(c), then there exists an exact $…

We show the flexibility of the metric entropy and obtain additional restrictions on the topological entropy of geodesic flow on closed surfaces of negative Euler characteristic with smooth non-positively curved Riemannian metrics with fixed…

Two recent articles \cite{ashtekar2015general, moncrief2019could} suggested an interesting dynamical mechanism within the framework of the vacuum Einstein flow (or Einstein-$\Lambda$ flow if a positive cosmological constant $\Lambda$ is…

For $G$ a closed subgroup of $S_{\infty}$, we provide an explicit characterization of the greatest $G$-ambit. Using this, we provide a precise characterization of when $G$ has metrizable universal minimal flow. In particular, each such…

We study the minimal spanning arborescence which is the directed analogue of the minimal spanning tree, with a particular focus on its infinite volume limit and its geometric properties. We prove that in a certain large class of transient…

We explore the relationship between Turing completeness and topological entropy of dynamical systems. We first prove that a natural class of Turing machines that we call "branching Turing machines" (which includes most of the known examples…

Non-smooth vector fields does not have necessarily the property of uniqueness of solution passing through a point and this is responsible to enrich the behavior of the system. Even on the plane non-smooth vector fields can be chaotic, a…

We show that an electric field parallel to an electrically neutral surface can generate flow of electrolytic mixtures in small channels. We term this solvo-osmotic flow, since the flow is induced by the asymmetric preferential solvation of…

Furstenberg's flow on the infinite-dimensional torus $\mathbb{T}^\omega$ is defined by \[ T (x_1, x_2, \ldots, x_\nu, \ldots) = (x_1 + \alpha, x_2 + h(x_1), \ldots, x_\nu + h(x_1 + (\nu-2)\beta), \ldots) \] with $\alpha\in \mathbb{R}$…

We derive an upper bound on the waiting time for a variational weak solution to Inverse Mean Curvature Flow in $\mathbb{R}^{n+1}$ to become star-shaped. As a consequence, we demonstrate that any connected surface moving by the flow which is…

Motivated by the well-known phase-space portrait of the nonlinear pendulum, the purpose of this paper is to obtain convergence rates in the ergodic theorem for flows in the plane that have arbitrarily slow trajectories. Considering bounded…

In this article, we prove the mean convex neighborhood conjecture for the mean curvature flow of surfaces in $\mathbb{R}^3$. Namely, if the flow has a spherical or cylindrical singularity at a space-time point $X=(x,t)$, then there exists a…

Motivated by Mather theory of minimizing measures for symplectic twist dynamics, we study conformally symplectic flows on a cotangent bundle. These dynamics are the most general dynamics for which it makes sense to look at (asymptotic)…

For a geodesic flow on a negatively curved Riemannian manifold $M$ and some subset $A\subset T^1M$, we study the limit $A$-exceptional set, that is the set of points whose $\omega$-limit do not intersect $A$. We show that if the topological…

Katok conjectured that every $C^{2}$ diffeomorphism $f$ on a Riemannian manifold has the intermediate entropy property, that is, for any constant $c \in[0, h_{top}(f))$, there exists an ergodic measure $\mu$ of $f$ satisfying…

Let a flow $T_t$ preserve an ergodic probability measure $\mu$, $\int f\,d\mu=0$, and $\mu(A)>0$. Then for almost all $x\in A$, for which $f(x)\neq 0$, there is a sequence ${t_k}\to \infty$ such that $T_{t_k}x\in A$ and $\int_0^{t_k}…

We consider perturbations of interval maps with indifferent fixed points, which we refer to as wobbly interval intermittent maps, for which stable laws for general H\"older observables fail. We obtain limit laws for such maps and H\"older…

We prove that sufficiently low-entropy closed hypersurfaces can be perturbed so that their mean curvature flow encounters only spherical and cylindrical singularities. Our theorem applies to all closed surfaces in $\mathbb{R}^3$ with…

We consider the topological dynamics of the automorphism group of a particular sparse graph M_1 resulting from an ab initio Hrushovski construction. We show that minimal subflows of the flow of linear orders on M_1 have all orbits meagre,…