arXiv subjects

Anastasios Stylianou

Publications and source records attributed to Anastasios Stylianou.

2 recordsLinked to original sources

arXiv2020

Statistics of multipliers for hyperbolic rational maps

In this article, we consider a counting problem for orbits of hyperbolic rational maps on the Riemann sphere, where constraints are placed on the multipliers of orbits. Using arguments from work of Dolgopyat, we consider varying and potentially shrinking intervals, and obtain a result which resembles a local central limit theorem for the logarithm of the absolute value of the multiplier and an equidistribution theorem for the holonomies.

math.DS↗

arXiv2020

A typical number is extremely non-normal

Fix a positive integer $N\geq2$. For a real number $x\in[0,1]$ and a digit $i\in\{0, 1,...,N-1\}$, let $\Pi_i(x, n)$ denote the frequency of the digit $i$ among the first $n$ $N$-adic digits of $x$. It is well-known that for a typical (in the sense of Baire) $x\in[0, 1]$, the frequencies diverge as $n\rightarrow\infty$. In this paper we provide a substantial strengthening of this result. Namely, we show that for a typical $x\in[0, 1]$ any regular linear average of the sequence $(\Pi_i(x, n))_n$ also diverges spectacularly.

math.NT↗