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pro vyhledávání: '"Hare, Kevin"'
Autor:
Hare, Kevin G., Noytaptim, Chatchai
In this article, we study some potential theoretical and topological aspects of the generalized Mandelbrot set introduced by Baker and DeMarco. For $\alpha$ real, we study the set of all totally real algebraic parameters $c$ such that $\alpha$ is pre
Externí odkaz:
http://arxiv.org/abs/2405.10395
Autor:
Hare, Kevin G.
Let $\{S_1, S_2, \dots, S_n\}$ be an iterated function system on $\mathbb{R}$ with attractor $K$. It is known that if the iterated function system satisfies the weak separation property and $K = [0,1]$ then the iterated function system also satisfies
Externí odkaz:
http://arxiv.org/abs/2403.00693
Autor:
Hare, Kevin G., Vávra, Tomáš
In this paper we investigate $p$-adic self-similar sets and $p$-adic self-similar measures. We show that $p$-adic self-similar sets are $p$-adic path set fractals, and that the converse is not necessarily true. For $p$-adic self-similar sets and $p$-
Externí odkaz:
http://arxiv.org/abs/2307.07375
Autor:
Hare, Kevin G.
Let $c(x)$ be a monic integer polynomial with coefficients $0$ or $1$. Write $c(x) = a(x) b(x)$ where $a(x)$ and $b(x)$ are monic polynomials with non-negative real (not necessarily integer) coefficients. The unfair 0--1 polynomial conjecture states
Externí odkaz:
http://arxiv.org/abs/2307.07363
Autor:
Hare, Kevin G., Sidorov, Nikita
Let $C$ be the classical middle third Cantor set. It is well known that $C+C = [0,2]$ (Steinhaus, 1917). (Here $+$ denotes the Minkowski sum.) Let $U$ be the set of $z \in [0,2]$ which have a unique representation as $z = x + y$ with $x, y \in C$ (th
Externí odkaz:
http://arxiv.org/abs/2210.07671
Autor:
Hare, Kevin G.
Let $\mu$ be a self-similar measure satisfying the finite type condition. It is known that the set of attainable local dimensions for such a measure is a union of disjoint intervals, where some intervals may be degenerate points. Despite this, it has
Externí odkaz:
http://arxiv.org/abs/2201.12196
We study representations of integral vectors in a number system with a matrix base $M$ and vector digits. We focus on the case when $M$ is similar to $J_n$, the Jordan block of $1$ of size $n$. If $M=J_2$, we classify digit sets of size 2 allowing re
Externí odkaz:
http://arxiv.org/abs/2110.11937
Autor:
Hare, Kevin G., Sidorov, Nikita
Let $0< \lambda < \mu<1$ and $\lambda+\mu>1$. In this note we prove that for the vast majority of such parameters the top of the attractor $A_{\lambda,\mu}$ of the IFS $\{(\lambda x,\mu y), (\mu x+1-\mu, \lambda y+1-\lambda)\}$ is the graph of a cont
Externí odkaz:
http://arxiv.org/abs/2101.01798
Publikováno v:
In Journal of Combinatorial Theory, Series A February 2024 202
Autor:
Hare, Kevin G., Sidorov, Nikita
Publikováno v:
International Journal of Number Theory 17 (2021), Issue 6, pp. 1307 - 1321
In this paper we investigate the Galois conjugates of a Pisot number $q \in (m, m+1)$, $m \geq 1$. In particular, we conjecture that for $q \in (1,2)$ we have $|q'| \geq \frac{\sqrt{5}-1}{2}$ for all conjugates $q'$ of $q$. Further, for $m \geq 3$, w
Externí odkaz:
http://arxiv.org/abs/2010.01511