Related papers: BCZ map is weakly mixing

We apply lattice Boltzmann methods to study the relaxation of the velocity profile in binary fluids under shear during spinodal decomposition. In simple fluids, when a shear flow is applied on the boundaries of the system, the time required…

We construct a Poincar\'e map $\mathcal{P}_h$ for the positive horocycle flow on the modular surface $PSL(2,\mathbb{Z})\backslash \mathbb{H}$, and begin a systematic study of its dynamical properties. In particular we give a complete…

It is known that a Lipschitz continuous map from the Euclidean domain to a metric space is metrically differentiable almost everywhere. When the metric space is a Banach space dual to separable, the metric differential has its linear…

We show that the billiard in a regular polygon is weak mixing in almost every invariant surface, except in the trivial cases which give rise to lattices in the plane (triangle, square and hexagon). More generally, we study the problem of…

We study skew-maps given by a minimal homeomorphism on the basis and a cocycle of affine isometries on the fibers. We call such a map a cylindrical vortex. We extend to this setting some classical results of Atkinson, Besicovitch,…

In a recent paper, Melbourne and Terhesiu [Operator renewal theory and mixing rates for dynamical systems with infinite measure, Invent. Math. 189 (2012), 61-110] obtained results on mixing and mixing rates for a large class of…

A new event mixing constraint, namely invariant-mass/energy hierarchy correspondence (IMEHC) cut, is introduced for the low-multiplicity event mixing technique for the purpose of measuring Bose-Einstein correlations (BEC) in exclusive…

Understanding Earth's core dynamics over millennial timescales requires models that jointly describe the evolution of the geomagnetic field and core surface flow, while accommodating the sparse, irregular, and uncertain nature of…

This paper will study topological, geometrical and measure-theoretical properties of the real Fibonacci map. Our goal was to figure out if this type of recurrence really gives any pathological examples and to compare it with the infinitely…

We prove that there exists a residual set of (non-rational) polygons such the billiard flow is weakly mixing with respect to the Liouville measure (on the unit tangent bundle to the billiard). This follows, via a Baire category argument,…

Montgomery in 1973 introduced the pair correlation method to study the vertical distribution of Riemann zeta-function zeros. This work assumed the Riemann Hypothesis (RH). One striking application was a short proof that at least 2/3 of…

We employ the curve shortening flow to establish three new results on the dynamics of geodesic flows of closed Riemannian surfaces. The first one is the stability, under $C^0$-small perturbations of the Riemannian metric, of certain flat…

We re-examine the theoretical uncertainty in the Standard Model expression for $B^0$-$\bar{B}^0$ mixing. We focus on lattice calculations of the ratio $\xi$, needed to relate the oscillation frequency of $B^0_s$-$\bar{B}^0_s$ mixing to the…

This paper provides a unified framework connecting dynamical systems with tools from topological data analysis and geometric topology and inspires new interactions among dynamical systems, topology, and nonlinear analysis. To this end, we…

In this paper the theory of uniformly convex metric spaces is developed. These spaces exhibit a generalized convexity of the metric from a fixed point. Using a (nearly) uniform convexity property a simple proof of reflexivity is presented…

For H\'enon maps, Bianchi and Dinh recently proved the exponential mixing of all orders for the measure of maximal entropy and, as a consequence of the recent work of Bj\"orklund and Gorodnik, the CLT for H\"older observables. We extend…

We consider the horocyclic flow corresponding to a (topologically mixing) Anosov flow or diffeomorphism, and establish the uniqueness of transverse quasi-invariant measures with H\"older Jacobians. In the same setting, we give a precise…

In L.W. Flinn's PhD thesis published in 1972, the author conjectured that weakly expansive flows are also expansive flows. In this paper we use the horocycle flow on compact Riemann surfaces of constant negative curvature to show that…

The aim of this work is to prove $C^1$ weak Palis conjecture for nonsingular flows. Weak Palis conjecture claims that a generic vector field either is Morse-Smale or exhibits horseshoes. Central model is come up with by Crovisier to obtain…

The pattern dynamics of the one-way coupled logistic lattice which can serve as a phenomenological model for open flow is investigated and shown to be extremely rich. For medium and large coupling strengths, we find spatially periodic,…