Zobrazeno 1 - 10
of 682
pro vyhledávání: '"A. Algom"'
Autor:
Algom, Amir, Shmerkin, Pablo
Let $\nu$ be a self similar measure on $\mathbb{R}^d$, $d\geq 2$, and let $\pi$ be an orthogonal projection onto a $k$-dimensional subspace. We formulate a criterion on the action of the group generated by the orthogonal parts of the IFS on $\pi$, an
Externí odkaz:
http://arxiv.org/abs/2407.16262
Let $\Phi$ be a $C^\omega (\mathbb{C})$ self-conformal IFS on the plane, satisfying some mild non-linearity and irreducibility conditions. We prove a uniform spectral gap estimate for the transfer operator corresponding to the derivative cocycle and
Externí odkaz:
http://arxiv.org/abs/2407.11688
Autor:
Algom, Amir, Wang, Zhiren
In 2017 Tao proposed a variant Sarnak's M\"{o}bius disjointness conjecture with logarithmic averaging: For any zero entropy dynamical system $(X,T)$, $\frac{1}{\log N} \sum_{n=1} ^N \frac{f(T^n x) \mu (n)}{n}= o(1)$ for every $f\in \mathcal{C}(X)$ an
Externí odkaz:
http://arxiv.org/abs/2406.06956
We prove a van der Corput lemma for non-atomic self-similar measures $\mu$. As an application, we show that the correlations of all finite orders of $( x^n \mod 1 )_{n\geq 1}$ converge to the Poissonian model for $\mu$-a.e. $x$, assuming $x>1$. We al
Externí odkaz:
http://arxiv.org/abs/2401.01120
We show that every self conformal measure with respect to a $C^2 (\mathbb{R})$ IFS $\Phi$ has polynomial Fourier decay under some mild and natural non-linearity conditions. In particular, every such measure has polynomial decay if $\Phi$ is $C^\omega
Externí odkaz:
http://arxiv.org/abs/2306.01275
Autor:
Algom, Amir, Wu, Meng
Let $F\subseteq [0,1]^2$ be a Bedford-McMullen carpet defined by exponents $m>n$, that projects to $[0,1]$ on the $y$-axis. We show that under mild conditions on $F$, there are many non principle lines $\ell$ such that $\dim^* F\cap \ell = \dim^* F -
Externí odkaz:
http://arxiv.org/abs/2303.17197
Publikováno v:
Frontiers in Psychology, Vol 15 (2024)
The effect known as the spatial-numerical association of response codes (SNARC) documents fast reaction to small numbers with a response at the left and to large numbers with a response at the right. The common explanation appeals to a hypothetical m
Externí odkaz:
https://doaj.org/article/fc3125a2a0b44a648c1cf3d980272f48
Autor:
Algom, Amir, Wang, Zhiren
Sarnak's M\"{o}bius disjointness conjecture asserts that for any zero entropy dynamical system $(X,T)$, $\frac{1}{N} \sum_{n=1} ^N f(T^n x) \mu (n)= o(1)$ for every $f\in \mathcal{C}(X)$ and every $x\in X$. We construct examples showing that this $o(
Externí odkaz:
http://arxiv.org/abs/2202.09491
Publikováno v:
Adv. Math. 399 (2022), Paper No. 108276, 17 pp
Let $\lbrace f_i(x)=s_i \cdot x+t_i \rbrace$ be a self-similar IFS on $\mathbb{R}$ and let $\beta >1$ be a Pisot number. We prove that if $\frac{\log |s_i|}{\log \beta}\notin \mathbb{Q}$ for some $i$ then for every $C^1$ diffeomorphism $g$ and every
Externí odkaz:
http://arxiv.org/abs/2111.10082
We prove that the Fourier transform of a self conformal measure on $\mathbb{R}$ decays to $0$ at infinity at a logarithmic rate, unless the following holds: The underlying IFS is smoothly conjugated to an IFS that both acts linearly on its attractor
Externí odkaz:
http://arxiv.org/abs/2109.13017