Zobrazeno 1 - 10
of 91
pro vyhledávání: '"28A80, 37C45"'
Autor:
Rapaport, Ariel
We extend Hochman's work on exponentially separated self-similar measures on $\mathbb{R}$ to the real analytic setting. More precisely, let $\Phi=\left\{ \varphi_{i}\right\} _{i\in\Lambda}$ be an iterated function system on $I:=[0,1]$ consisting of r
Externí odkaz:
http://arxiv.org/abs/2412.16753
Autor:
Huo, Qiang
Tsukamoto (2022) introduced the notion of Bedford-McMullen carpet system, a subsystem of $([0,1]^{\mathbb{N}}\times[0,1]^{\mathbb{N}},shift)$ whose metric mean dimension and mean Hausdorff dimension does not coincide in general. The aim of this paper
Externí odkaz:
http://arxiv.org/abs/2412.02278
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
In this paper, we give the Assouad dimension formula and the upper bound of the lower dimension for homogeneous Moran sets under the condition $\sup_{k\ge 1}\{n_{k}\}<+\infty$. We also give the Assouad spectrum and the lower spectrum formulas for Can
Externí odkaz:
http://arxiv.org/abs/2407.14837
Autor:
Rapaport, Ariel, Ren, Haojie
For $(\lambda_{1},...,\lambda_{d})=\lambda\in(0,1)^{d}$ with $\lambda_{1}>...>\lambda_{d}$, denote by $\mu_{\lambda}$ the Bernoulli convolution associated to $\lambda$. That is, $\mu_{\lambda}$ is the distribution of the random vector $\sum_{n\ge0}\p
Externí odkaz:
http://arxiv.org/abs/2406.05495
Autor:
Rutar, Alex
We provide a self-contained exposition of the well-known multifractal formalism for self-similar measures satisfying the strong separation condition. At the heart of our method lies a pair of quasiconvex optimization problems which encode the paramet
Externí odkaz:
http://arxiv.org/abs/2312.08974
Autor:
Rapaport, Ariel
Let $\Phi:=\left\{ (x_{1},...,x_{d})\rightarrow\left(r_{i,1}x_{1}+a_{i,1},...,r_{i,d}x_{d}+a_{i,d}\right)\right\} _{i\in\Lambda}$ be an affine diagonal IFS on $\mathbb{R}^{d}$. Suppose that for each $1\le j_{1}
Externí odkaz:
http://arxiv.org/abs/2309.03985
Autor:
Bárány, Balázs, Käenmäki, Antti
We study the dimension of the attractor and quasi-Bernoulli measures of parametrized families of iterated function systems of non-conformal and non-affine maps. We introduce a transversality condition under which, relying on a weak Ledrappier-Young f
Externí odkaz:
http://arxiv.org/abs/2308.09590
We consider generic 1-parameter unfoldings of parabolic vector fields. It is known that the box dimension of orbits of their time-one maps is discontinuous at the bifurcation value. Here, we expand asymptotically the Lebesgue measure of the epsilon-n
Externí odkaz:
http://arxiv.org/abs/2304.07914