Zobrazeno 1 - 10
of 22
pro vyhledávání: '"Bill Mance"'
We consider the complexity of special $\alpha$-limit sets, a kind of backward limit set for non-invertible dynamical systems. We show that these sets are always analytic, but not necessarily Borel, even in the case of a surjective map on the unit squ
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::6ecc8b0489f2b14419c7e6955cb73ae2
http://arxiv.org/abs/2011.05509
http://arxiv.org/abs/2011.05509
A Cantor series expansion for a real number $x$ with respect to a basic sequence $Q=(q_1,q_2,\dots)$, where $q_i \geq 2$, is a representation of the form $x=a_0 + \sum_{i=1}^\infty \frac{a_i}{q_1q_2\cdots q_i}$ where $0 \leq a_i
Comment: 22 page
Comment: 22 page
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::65edca62d0f230e0cbd98895e06875f3
Autor:
Bill Mance, Dylan Airey
Publikováno v:
Journal of Fractal Geometry. 3:163-186
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::81b694e76f341eb33103f0d6214756cd
https://doi.org/10.4171/jfg/33
https://doi.org/10.4171/jfg/33
We study the Borel complexity of sets of normal numbers in several numeration systems. Taking a dynamical point of view, we offer a unified treatment for continued fraction expansions and base $r$ expansions, and their various generalisations: genera
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https://explore.openaire.eu/search/publication?articleId=doi_dedup___::38349b78d633dc442314c83594ffa3e5
http://arxiv.org/abs/1811.04450
http://arxiv.org/abs/1811.04450
Autor:
Veekesh Kumar, Bill Mance
In this article we discuss the transcendence of certain infinite sums and products by using the Subspace theorem. In particular we improve the result of Han\v{c}l and Rucki \cite{hancl3}.
Comment: 14 pages
Comment: 14 pages
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::8e13a9e214de39fecf6c95c010fe027c
http://arxiv.org/abs/1807.09646
http://arxiv.org/abs/1807.09646
Autor:
Dylan Airey, Bill Mance
Publikováno v:
Advances in Mathematics. 279:372-404
We explore in depth the number theoretic and statistical properties of certain sets of numbers arising from their Cantor series expansions. As a direct consequence of our main theorem we deduce numerous new results as well as strengthen known ones.
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https://explore.openaire.eu/search/publication?articleId=doi_dedup___::d7b7978f1e978ea1ce37942d4dd83763
https://doi.org/10.1016/j.aim.2015.03.008
https://doi.org/10.1016/j.aim.2015.03.008
Publikováno v:
Bulletin of the Australian Mathematical Society. 92:205-213
We provide a closed formula of Bowen type for the Hausdorff dimension of a very general shrinking target scheme generated by the nonautonomous dynamical system on the interval$[0,1)$, viewed as$\mathbb{R}/\mathbb{Z}$, corresponding to a given method
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::ec767bbbd300322d5bee81b9c2bb8115
https://doi.org/10.1017/s0004972715000441
https://doi.org/10.1017/s0004972715000441
Autor:
Bill Mance
Publikováno v:
Acta Mathematica Hungarica. 144:449-493
Suppose that $${{(P, Q) \in {\mathbb{N}_{2}^\mathbb{N}} \times {\mathbb{N}_{2}^\mathbb{N}}}}$$ and x = E 0.E 1 E 2 · · · is the P-Cantor series expansion of $${x \in \mathbb{R}}$$ . We define $$\psi_{P,Q}(x) := {\sum_{n=1}^{\infty}} \frac{{\rm min
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::a84c4f482ce26bf4bf83351a08415820
https://doi.org/10.1007/s10474-014-0456-7
https://doi.org/10.1007/s10474-014-0456-7
Autor:
Jimmy Tseng, Bill Mance
Publikováno v:
Acta Arithmetica. 158:33-47
This is the author accepted manuscript. The final version is available from Polskiej Akademii Nauk, Instytut Matematyczny via the DOI in this record.
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::51c3eefa145e684c55009a186c2197c1
https://doi.org/10.4064/aa158-1-2
https://doi.org/10.4064/aa158-1-2
Let $\mathscr{N}(b)$ be the set of real numbers which are normal to base $b$. A well-known result of H. Ki and T. Linton is that $\mathscr{N}(b)$ is $\boldsymbol{\Pi}^0_3$-complete. We show that the set $\mathscr{N}(b)$ of reals which preserve $\math
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::56c61521b3ee05c948335ca4b47f3430
http://arxiv.org/abs/1609.08702
http://arxiv.org/abs/1609.08702