Generic Birkhoff Spectra

Zoltán Buczolich, Balázs Maga, Ryo Moore

Suppose that $\Omega =\{0,1{\}}^{\mathbb{N}}$ and $\sigma$ is the one-sided shift. The Birkhoff spectrum $ \displaystyle S_{f}( α)=\dim_{H}\Big \{ ω\in Ω:\lim_{N \to \infty} \frac{1}{N} \s…