# r#"<?xml version="1.0" encoding="UTF-8"?>
# <feed xmlns="http://www.w3.org/2005/Atom">
# <link href="http://arxiv.org/api/query?search_query%3D%26id_list%3D2206.06921%26start%3D0%26max_results%3D10" rel="self" type="application/atom+xml"/>
# <title type="html">ArXiv Query: search_query=&id_list=2206.06921&start=0&max_results=10</title>
# <id>http://arxiv.org/api/G79xvO0tGdRYEe8vHn0XokC5HLI</id>
# <updated>2025-08-21T00:00:00-04:00</updated>
# <opensearch:itemsPerPage xmlns:opensearch="http://a9.com/-/spec/opensearch/1.1/">10</opensearch:itemsPerPage>
# <opensearch:totalResults xmlns:opensearch="http://a9.com/-/spec/opensearch/1.1/">1</opensearch:totalResults>
# <opensearch:startIndex xmlns:opensearch="http://a9.com/-/spec/opensearch/1.1/">0</opensearch:startIndex>
# <entry>
# <id>http://arxiv.org/abs/2206.06921v3</id>
# <updated>2024-08-12T11:56:51Z</updated>
# <published>2022-06-14T15:35:46Z</published>
# <title>Attainable forms of Assouad spectra</title>
# <summary> Let $d\in\mathbb{N}$ and let $\varphi\colon(0,1)\to[0,d]$. We prove that
# there exists a set $F\subset\mathbb{R}^d$ such that
# $\operatorname{dim}_A^\theta F=\varphi(\theta)$ for all $\theta\in(0,1)$ if and
# only if for every $0<\lambda<\theta<1$, \[0\leq
# (1-\lambda)\varphi(\lambda)-(1-\theta)\varphi(\theta)\leq
# (\theta-\lambda)\varphi\Bigl(\frac{\lambda}{\theta}\Bigr).\] In particular, the
# following behaviours which have not previously been witnessed in any examples
# are possible: the Assouad spectrum can be non-monotonic on every open set, and
# can fail to be H\"older in a neighbourhood of 1.
# </summary>
# <author>
# <name>Alex Rutar</name>
# </author>
# <arxiv:doi xmlns:arxiv="http://arxiv.org/schemas/atom">10.1512/iumj.2024.73.9928</arxiv:doi>
# <link title="doi" href="http://dx.doi.org/10.1512/iumj.2024.73.9928" rel="related"/>
# <arxiv:comment xmlns:arxiv="http://arxiv.org/schemas/atom">25 pages, 5 figures. v3: Many typo fixes and substantially improved
# exposition, especially in non-monotonic construction. Some numbering changes
# from v2. Results unchanged</arxiv:comment>
# <arxiv:journal_ref xmlns:arxiv="http://arxiv.org/schemas/atom">Indiana Univ. Math. J. 73 (2024), 1331-1356</arxiv:journal_ref>
# <link href="http://arxiv.org/abs/2206.06921v3" rel="alternate" type="text/html"/>
# <link title="pdf" href="http://arxiv.org/pdf/2206.06921v3" rel="related" type="application/pdf"/>
# <arxiv:primary_category xmlns:arxiv="http://arxiv.org/schemas/atom" term="math.CA" scheme="http://arxiv.org/schemas/atom"/>
# <category term="math.CA" scheme="http://arxiv.org/schemas/atom"/>
# <category term="math.DS" scheme="http://arxiv.org/schemas/atom"/>
# <category term="math.MG" scheme="http://arxiv.org/schemas/atom"/>
# <category term="28A80 (Primary) 39B62 (Secondary)" scheme="http://arxiv.org/schemas/atom"/>
# </entry>
# </feed>"#;