Let $(\Sigma,\sigma)$ be one-sided full shift over a finite alphabet. Let $\phi:\Sigma\to\R$ be a continuous potential and let $w:\N\to\R$ a bounded function. We consider the sets
\[
L(\alpha) := \{\omega\in\Sigma; \lim_{n\to\infty} \frac 1n \sum_{i=0}^{n-1} w(i) \phi(\sigma^i\omega)=\alpha\}.
\]
Per analogiam with the usual multifractal formalism, we will investigate the function $\alpha \to h_{\rm top} L(\alpha)$ and prove some properties (as well as provide examples showing some other properties do not hold).
It is a joint work with Ruxi Shi from IMPAN.
Weighted Birkhoff spectra
22.01.2020 13:30 - 15:15
Organiser:
H. Bruin, R. Zweimüller
Location: