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pro vyhledávání: '"Hochman, Michael A."'
For self-similar sets $X,Y\subseteq \mathbb{R}$, we obtain new results towards the affine embeddings conjecture of Feng-Huang-Rao (2014), and the equivalent weak intersections conjecture. We show that the conjecture holds when the defining maps of $X
Externí odkaz:
http://arxiv.org/abs/2410.19648
Autor:
Hochman, Michael
We show that the Feng-Xiong lower bound of $1/2$ for the box dimension of $\alpha\beta$-sets is tight. We also study how much of an $\alpha\beta$-orbit ``carries the dimension'': deleting an arbitararily small positive density set of times can cause
Externí odkaz:
http://arxiv.org/abs/2410.19640
Autor:
Hochman, Michael
We show that there exist $\mathbb{Z}^{2}$ symbolic systems that are strongly irreducible and have no (fully) periodic points
Comment: 36 pages, 4 figures
Comment: 36 pages, 4 figures
Externí odkaz:
http://arxiv.org/abs/2401.02273
Autor:
Hochman, Michael
Let $(X,\mathcal{B},\mu,T)$ be a probability-preserving system with $X$ compact and $T$ a homeomorphism. We show that if every point in $X\times X$ is two-sided recurrent, then $h_{\mu}(T)=0$, resolving a problem of Benjamin Weiss, and that if $h_{\m
Externí odkaz:
http://arxiv.org/abs/2312.15812
Autor:
Hochman, Michael
We show that a topological Cantor set in the line has at most countably many real-analytic, onto self-maps.
Comment: 9 pages
Comment: 9 pages
Externí odkaz:
http://arxiv.org/abs/2312.15810
SOHO State of the Art Updates and Next Questions: An Update on Higher Risk Myelodysplastic Syndromes
Autor:
Hochman, Michael J., DeZern, Amy E.
Publikováno v:
In Clinical Lymphoma, Myeloma and Leukemia September 2024 24(9):573-582
Autor:
Hochman, Michael
Publikováno v:
Israel Journal of Mathematics, volume 251, pages 527-539 (2022)
This note contains a new proof of Host's equidistribution theorem for multiplicatively independent endomorphisms of $\mathbb{R}/\mathbb{Z}$. The method is a simplified version of our upcoming work on equidistribution under toral automorphisms and is
Externí odkaz:
http://arxiv.org/abs/2103.08938
Publikováno v:
In Clinical Lymphoma, Myeloma and Leukemia September 2024
Autor:
Hochman, Michael, Rapaport, Ariel
We prove that if $\mu$ is a self-affine measure in the plane whose defining IFS acts totally irreducibly on $\mathbb{RP}^1$ and satisfies an exponential separation condition, then its dimension is equal to its Lyapunov dimension. We also treat a clas
Externí odkaz:
http://arxiv.org/abs/1904.09812
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