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pro vyhledávání: '"Alexia Yavicoli"'
Autor:
Alexia Yavicoli
Publikováno v:
Mathematical and Computational Applications, Vol 27, Iss 6, p 111 (2022)
In this article, we introduce a notion of size for sets, called the thickness, that can be used to guarantee that two Cantor sets intersect (the Gap Lemma) and show a connection among thickness, Schmidt games and patterns. We work mostly in the real
Externí odkaz:
https://doaj.org/article/2ad05d52823b45318ac3f7f83d740970
Autor:
Alexia Yavicoli
Publikováno v:
Israel Journal of Mathematics. 244:95-126
We introduce a connection between Newhouse thickness and patterns through a variant of Schmidt’s game introduced by Broderick, Fishman and Simmons. This yields an explicit, robust and checkable condition that ensures that a Cantor set in the real l
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::3af43613e066be87bf1afc09c2ff3a10
https://doi.org/10.1007/s11856-021-2173-6
https://doi.org/10.1007/s11856-021-2173-6
Publikováno v:
Revista Matemática Iberoamericana. 38:295-322
We show that given $\alpha \in (0, 1)$ there is a constant $c=c(\alpha) > 0$ such that any planar $(\alpha, 2\alpha)$-Furstenberg set has Hausdorff dimension at least $2\alpha + c$. This improves several previous bounds, in particular extending a res
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::d2e9fc11cb84754aa3d7bb6967e20f1d
https://doi.org/10.4171/rmi/1281
https://doi.org/10.4171/rmi/1281
Autor:
Alexia Yavicoli, Ursula Molter
Publikováno v:
Mathematical Proceedings of the Cambridge Philosophical Society. 168:57-73
Given any dimension function $h$, we construct a perfect set $E \subseteq \mathbb{R}$ of zero $h$-Hausdorff measure, that contains any finite polynomial pattern. This is achieved as a special case of a more general construction in which we have a fam
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::9fff189d7026a239aaba3eedaf575c68
https://doi.org/10.1017/s0305004118000567
https://doi.org/10.1017/s0305004118000567
We provide quantitative estimates for the supremum of the Hausdorff dimension of sets in the real line which avoid $\varepsilon$-approximations of arithmetic progressions. Some of these estimates are in terms of Szemer\'{e}di bounds. In particular, w
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::c6565da1c566eb0ac1bf3ad1fd01f1cb
http://arxiv.org/abs/1910.10074
http://arxiv.org/abs/1910.10074
Publikováno v:
CONICET Digital (CONICET)
Consejo Nacional de Investigaciones Científicas y Técnicas
instacron:CONICET
Consejo Nacional de Investigaciones Científicas y Técnicas
instacron:CONICET
We prove preservation of $L^q$ dimensions (for $1
Comment: 30 pages, no figures
Comment: 30 pages, no figures
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::9ecea1a5d91185bbe2fbf85457225ed0
https://doi.org/10.1088/0951-7715/29/9/2609
https://doi.org/10.1088/0951-7715/29/9/2609
Publikováno v:
Nonlinearity; Sep2016, Vol. 29 Issue 9, p1-1, 1p