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of 23
pro vyhledávání: '"Bersudsky, Michael"'
We extend Ratner's theorem on equidistribution of individual orbits of unipotent flows on finite volume homogeneous spaces of Lie groups to trajectories of non-contracting curves definable in polynomially bounded o-minimal structures. To be precise,
Externí odkaz:
http://arxiv.org/abs/2407.04935
Autor:
Bersudsky, Michael, Xing, Hao
We study the limiting distribution of dense orbits of a lattice subgroup $\Gamma\le \text{SL}(m+1,\mathbb{R})$ acting on $H\backslash\text{SL}(m+1,\mathbb{R})$, with respect to a filtration of growing norm balls. The novelty of our work is that the g
Externí odkaz:
http://arxiv.org/abs/2307.12085
Autor:
Bersudsky, Michael, Xing, Hao
We study the distribution of orbits of a lattice $\Gamma\leq\text{SL}(3,\mathbb R)$ in the moduli space $X_{2,3}$ of covolume one rank-two discrete subgroups in $\mathbb R^3$. Each orbit is dense, and our main result is the limiting distribution of t
Externí odkaz:
http://arxiv.org/abs/2305.04132
Autor:
Bersudsky, Michael, Shapira, Uri
We compute the statistics of $SL_{d}(\mathbb{Z})$ matrices lying on level sets of an integral polynomial defined on $SL_{d}(\mathbb{R})$, a result that is a variant of the well known theorem proved by Linnik about the equidistribution of radially pro
Externí odkaz:
http://arxiv.org/abs/2107.02159
Autor:
Bersudsky, Michael
It is known that the image in $\mathbb{R}^{2}/\mathbb{Z}^{2}$ of a circle of radius $\rho$ in the plane becomes equidistributed as $\rho\to\infty$. We consider the following sparse version of this phenomenon. Starting from a sequence of radii $\left\
Externí odkaz:
http://arxiv.org/abs/2003.04112
Autor:
Bersudsky, Michael
We prove existence and compute the limiting distribution of the image of rank-$\left(d-1\right)$ primitive subgroups of $\mathbb{Z}^{d}$ of large covolume in the space $X_{d-1,d}$ of homothety classes of rank-$\left(d-1\right)$ discrete subgroups of
Externí odkaz:
http://arxiv.org/abs/1908.07165
The nodal set of a Laplacian eigenfunction forms a partition of the underlying manifold or graph. Another natural partition is based on the gradient vector field of the eigenfunction (on a manifold) or on the extremal points of the eigenfunction (on
Externí odkaz:
http://arxiv.org/abs/1805.07612
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We find the Courant-sharp Neumann eigenvalues of the Laplacian on some 2-rep-tile domains. In $\R^{2}$ the domains we consider are the isosceles right triangle and the rectangle with edge ratio $\sqrt{2}$ (also known as the A4 paper). In $\R^{n}$ the
Externí odkaz:
http://arxiv.org/abs/1507.03410
Akademický článek
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