Zobrazeno 1 - 10
of 138
pro vyhledávání: '"Kanigowski, Adam"'
Publikováno v:
Int. Math. Res. Not. IMRN (2), 11488-11512, 2024
We consider vanishing properties of exponential sums of the Liouville function $\lambda$ of the form $$ \lim_{H\to\infty}\limsup_{X\to\infty}\frac{1}{\log X}\sum_{m\leq X}\frac{1}{m}\sup_{\alpha\in C}\bigg|\frac{1}{H}\sum_{h\leq H}\lambda(m+h)e^{2\pi
Externí odkaz:
http://arxiv.org/abs/2310.05528
We construct a smooth area preserving flow on a genus 2 surface with exactly one open uniquely ergodic component, that is asymmetrically bounded by separatrices of non-degenerate saddles and that is nevertheless not mixing.
Comment: 50 pages, 4
Comment: 50 pages, 4
Externí odkaz:
http://arxiv.org/abs/2308.01247
We consider generalized $(T, T^{-1})$ transformations such that the base map satisfies a multiple mixing local limit theorem and anticoncentration large deviation bounds and in the fiber we have $\mathbb{R}^d$ actions with $d=1$ or $2$ which are expo
Externí odkaz:
http://arxiv.org/abs/2305.04246
We construct conservative analytic flows of zero metric entropy which satisfy the classical central limit theorem.
Externí odkaz:
http://arxiv.org/abs/2210.10121
Autor:
Forni, Giovanni, Kanigowski, Adam
We discuss several counterexamples to a rigidity conjecture of K. Khanin, which states that under some quantitative condition on non-existence of periodic orbits, $C^0$ conjugacy implies $C^1$ (even $C^\infty$) conjugacy. We construct examples of non
Externí odkaz:
http://arxiv.org/abs/2108.09584
Let $f$ be a $C^{1+\alpha}$ diffeomorphism of a compact manifold $M$ preserving a smooth measure $\mu$. We show that if $f:(M,\mu)\to (M,\mu)$ is exponentially mixing then it is Bernoulli.
Externí odkaz:
http://arxiv.org/abs/2106.03147
We prove Veech's conjecture on the equivalence of Sarnak's conjecture on M\"obius orthogonality with a Kolmogorov type property of Furstenberg systems of the M\''obius function. This yields a combinatorial condition on the M\"obius function itself wh
Externí odkaz:
http://arxiv.org/abs/2105.11737
Autor:
Kanigowski, Adam, Lemańczyk, Mariusz
This is a survey on spectral theory of dynamical systems.
Externí odkaz:
http://arxiv.org/abs/2006.11616
In this paper we exhibit new classes of smooth systems which satisfy the Central Limit Theorem (CLT) and have (at least) one of the following properties: (1) zero entropy; (2) weak but not strong mixing; (3) (polynomially) mixing but not $K$; (4) $K$
Externí odkaz:
http://arxiv.org/abs/2006.02191
Autor:
Kanigowski, Adam
We consider a class of smooth mixing flows $T^{\alpha,\gamma}$ on $\mathbb{T}^2$ with one degenerated fixed point $x_0\in \mathbb{T}^2$ of power type $\gamma\in (-1,0)$. We prove that for a $G_\delta$ dense set of $\alpha\in \mathbb{T}$, a prime numb
Externí odkaz:
http://arxiv.org/abs/2005.09403