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pro vyhledávání: '"Amir Algom"'
Autor:
AMIR ALGOM, ZHIREN WANG
Publikováno v:
Ergodic Theory and Dynamical Systems. :1-18
Sarnak’s Möbius disjointness conjecture asserts that for any zero entropy dynamical system $(X,T)$ , $({1}/{N})\! \sum _{n=1}^{N}\! f(T^{n} x) \mu (n)= o(1)$ for every $f\in \mathcal {C}(X)$ and every $x\in X$ . We construct examples showing that
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::15f117d0371427ba18a3cfb708909c67
https://doi.org/10.1017/etds.2022.61
https://doi.org/10.1017/etds.2022.61
Autor:
Amir Algom
Publikováno v:
Transactions of the American Mathematical Society. 373:8439-8462
Let $\mu$ be a probability measure on $\mathbb{R}/\mathbb{Z}$ that is ergodic under the $\times p$ map, with positive entropy. In 1995, Host showed that if $\gcd(m,p)=1$ then $\mu$ almost every point is normal in base $m$. In 2001, Lindenstrauss show
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::6aec57365dc33a11e2f8727f33616f57
https://doi.org/10.1090/tran/8173
https://doi.org/10.1090/tran/8173
Autor:
Meng Wu, Amir Algom
Let $F$ be a Bedford–McMullen carpet defined by independent integer exponents. We prove that for every line $\ell \subseteq \mathbb{R}^2$ not parallel to the major axes, $$\begin{align*} & \dim_H (\ell \cap F) \leq \max \left\lbrace 0,\, \frac{\dim
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::09a1656460bb527fc843712985c1282e
http://arxiv.org/abs/2107.02068
http://arxiv.org/abs/2107.02068
Autor:
Amir Algom
Let $$\nu $$ be a probability measure that is ergodic under the endomorphism $$(\times p, \times p)$$ of the torus $${\mathbb {T}}^2$$ , such that $$\dim \pi \mu < \dim \mu $$ for some non-principal projection $$\pi $$ . We show that, if both $$m\ne
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::9f53c46e9cbd6f9b0ccba535af38893c
Autor:
Amir Algom
Publikováno v:
Journal of Fractal Geometry. 5:339-350
Let $s\in (0,1)$, and let $F\subset \mathbb{R}$ be a self similar set such that $0 < \dim_H F \leq s$ . We prove that there exists $\delta= \delta(s) >0$ such that if $F$ admits an affine embedding into a homogeneous self similar set $E$ and $0 \leq
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::dee956dbb514c6ce300b1139f9e7b5e9
https://doi.org/10.4171/jfg/63
https://doi.org/10.4171/jfg/63
Publikováno v:
Advances in Mathematics. 393:108096
Let $\Phi$ be a $C^{1+\gamma}$ smooth IFS on $\mathbb{R}$, where $\gamma>0$. We provide mild conditions on the derivative cocycle that ensure that every self conformal measure is supported on points $x$ that are absolutely normal. That is, for intege
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::9134e6c0c2ed6219938a54074c051089
https://doi.org/10.1016/j.aim.2021.108096
https://doi.org/10.1016/j.aim.2021.108096
Autor:
Amir Algom, Michael Hochman
Publikováno v:
Ergodic Theory and Dynamical Systems. 39:577-603
Let$F\subseteq \mathbb{R}^{2}$be a Bedford–McMullen carpet defined by multiplicatively independent exponents, and suppose that either$F$is not a product set, or it is a product set with marginals of dimension strictly between zero and one. We prove
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::64b4a81a03cdf9cbf6a83ca0769ee130
https://doi.org/10.1017/etds.2017.46
https://doi.org/10.1017/etds.2017.46
Autor:
Amir Algom
Let $F$ be a Bedford-McMullen carpet defined by independent exponents. We prove that $\overline{\dim}_B (\ell \cap F) \leq \max \lbrace \dim^* F -1,0 \rbrace$ for all lines $\ell$ not parallel to the principal axes, where $\dim^*$ is Furstenberg's st
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::209d4ed0dcbbe0dcc7a98dfef58b9ff9
http://arxiv.org/abs/1811.07424
http://arxiv.org/abs/1811.07424
Autor:
Amir Algom
Let $F,E\subseteq \mathbb{R}^2$ be two self similar sets. First, assuming $F$ is generated by an IFS $\Phi$ with strong separation, we characterize the affine maps $g:\mathbb{R}^2 \rightarrow \mathbb{R}^2$ such that $g(F)\subseteq F$. Our analysis de
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::5a88bc0776b351a1265d1213bcf043b7
http://arxiv.org/abs/1709.03906
http://arxiv.org/abs/1709.03906