Contents Online
Mathematical Research Letters
Volume 9 (2002)
Number 3
The Pressure Function for Products of Non-negative Matrices
Pages: 363 – 378
DOI: https://dx.doi.org/10.4310/MRL.2002.v9.n3.a10
Authors
Abstract
Let $(\Sigma_A, \sigma)$ be a subshift of finite type and let $M(x)$ be a continuous function on $\Sigma_A$ taking values in the set of non-negative matrices. We extend the classical scalar pressure function to this new setting and prove the existence of the Gibbs measure and the differentiability of the pressure function. We are especially interested on the case where $M(x)$ takes finite values $M_1, \cdots, M_m$. The pressure function reduces to $P(q):=\lim_{n\rightarrow \infty}\frac{1}{n} \log \sum_{\hskip -2pt J \in \Sigma_{A, n}} \|M_J\|^q$. The expression is important when we consider the multifractal formalism for certain iterated function systems with overlaps.
Published 1 January 2002