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pro vyhledávání: '"Neunhäuserer, Jörg"'
Autor:
Neunhäuserer, Jörg
Non-homogeneous self-similar measures are generically absolute continuous in the domain of parameters for which the similarity dimension is larger than one, see \cite{[SSS]}. Using certain algebraic curves we construct here exceptional singular non-h
Externí odkaz:
http://arxiv.org/abs/2410.08785
Autor:
Neunhäuserer, Jörg
For $\alpha>1$ we represent a real number in $(0,1]$ in the form \[ \sum_{i=1}^{\infty}(\alpha-1)^{i-1}\alpha^{-(d_{1}+\dots+d_{i})}\] with $d_{i}\in\mathbb{N}$. We discuss ergodic theoretical and dimension theoretical aspects of this expansion. Furt
Externí odkaz:
http://arxiv.org/abs/2406.10919
Autor:
Neunhäuserer, Jörg
We show that for the base two expansion \[ x=\sum_{i=1}^{\infty}2^{-(d_{1}(x)+d_{2}(x)+\dots+d_{i}(x))}\] with $x\in(0,1]$ and $d_{i}(x)\in\mathbb{N}$ the set $A=\{x|\lim_{i\to\infty}d_{i}(x)=\infty\}$ has Hausdorff dimension zero, this is opposed to
Externí odkaz:
http://arxiv.org/abs/2201.09641
Autor:
Neunhäuserer, Jörg
Publikováno v:
Elemente der Mathematik, vol. 76, no.1., 1-3, 2021
We show that Somos' constant is universal in sense that is similar to the universality of the Khinchin constant. In addition we introduce generalized Somos' constants, which are universal in a similar sense.
Externí odkaz:
http://arxiv.org/abs/2006.02882
Autor:
Neunhäuserer, Jörg
We introduce and study expansions of real numbers with respect to two integer bases.
Comment: to appear: Rocky Mountain Journal of Mathematics
Comment: to appear: Rocky Mountain Journal of Mathematics
Externí odkaz:
http://arxiv.org/abs/2002.10824
Autor:
Neunhäuserer, Jörg
Publikováno v:
Mediterranean Journal of Mathematics, 18 (2), 1-8, 2021
We introduce and study non-uniform expansions of real numbers, given by two non-integer bases.
Externí odkaz:
http://arxiv.org/abs/1909.04414
Autor:
Neunhäuserer, Jörg
Publikováno v:
Tatra Mt. Math. Publ. 81, 1-8, 2022
We observe that a probability distribution supported by $\mathbb{N}$, induces a representation of real numbers in [0, 1) with digits in $\mathbb{N}$. We first study the Hausdorff dimension of sets with prescribed digits with respect to these represen
Externí odkaz:
http://arxiv.org/abs/1903.08559
Autor:
Neunhäuserer, Jörg
Publikováno v:
Acta Mathematica Hungarica, vol. 113 (4-4),333-343, 2006
In [8] we found a class of overlapping asymmetric self-similar measures on the real line, which are generically absolutely continuous with respect to the Lebesgue measure. Here we construct exceptional measures in this class being singular.
Externí odkaz:
http://arxiv.org/abs/1810.12622