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pro vyhledávání: '"Weiss, Barak"'
A classical argument was introduced by Khintchine in 1926 in order to exhibit the existence of totally irrational singular linear forms in two variables. This argument was subsequently revisited and extended by many authors. For instance, in 1959 Jar
Externí odkaz:
http://arxiv.org/abs/2409.15607
Let $K$ be a convex body in $\mathbb{R}^n$, let $L$ be a lattice with covolume one, and let $\eta>0$. We say that $K$ and $L$ form an $\eta$-smooth cover if each point $x \in \mathbb{R}^n$ is covered by $(1 \pm \eta) vol(K)$ translates of $K$ by $L$.
Externí odkaz:
http://arxiv.org/abs/2311.04644
We consider the horospherical foliation on any invariant subvariety in the moduli space of translation surfaces. This foliation can be described dynamically as the strong unstable foliation for the geodesic flow on the invariant subvariety, and geome
Externí odkaz:
http://arxiv.org/abs/2303.07188
Let M be an invariant subvariety in the moduli space of translation surfaces. We contribute to the study of the dynamical properties of the horocycle flow on M. In the context of dynamics on the moduli space of translation surfaces, we introduce the
Externí odkaz:
http://arxiv.org/abs/2301.12419
We introduce the notion of a zebra structure on a surface, which is a more general geometric structure than a translation structure or a dilation structure that still gives a directional foliation of every slope. We are concerned with the question of
Externí odkaz:
http://arxiv.org/abs/2301.03727
Autor:
Chaika, Jon, Weiss, Barak
Let $\mathcal{H}$ be a stratum of translation surfaces with at least two singularities, let $m_{\mathcal{H}}$ denote the Masur-Veech measure on $\mathcal{H}$, and let $Z_0$ be a flow on $(\mathcal{H}, m_{\mathcal{H}})$ obtained by integrating a Rel v
Externí odkaz:
http://arxiv.org/abs/2301.02483
Autor:
Shapira, Uri, Weiss, Barak
Let $\theta\in\mathbb{R}^d$. We associate three objects to each approximation $(p,q)\in \mathbb{Z}^d\times \mathbb{N}$ of $\theta$: the projection of the lattice $\mathbb{Z}^{d+1}$ to the hyperplane of the first $d$ coordinates along the approximatin
Externí odkaz:
http://arxiv.org/abs/2206.05329
Publikováno v:
In Advances in Mathematics August 2024 451
We define Ratner-Marklof-Strombergsson measures. These are probability measures supported on cut-and-project sets in R^d (d > 1) which are invariant and ergodic for the action of the groups ASL_d(R) or SL_d(R). We classify the measures that can arise
Externí odkaz:
http://arxiv.org/abs/2012.13299
Autor:
Chaika, Jon1 chaika@math.utah.edu, Weiss, Barak2 barakw@tauex.tau.ac.il
Publikováno v:
Forum of Mathematics, Pi. 4/2/2024, Vol. 12, p1-25. 25p.