The Pressure Function for Products of Non-negative Matrices

Details The Pressure Function for Products of Non-negative Matrices The Pressure Function for Products of Non-negative Matrices

2002-05-02

arxiv.org/abs/math/0205028v1

Mathematics

Dynamical Systems

Scientific paper

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 $M_1, ..., M_m$. The pressure function reduces to $P(q):=\lim_{n\to \infty}\frac{1}{n} \log \sum_{J \in \sum_{A, n}} \|M_J\|^q$. The expression is important when we consider the multifractal formalism for certain iterated function systems with overlaps.

Affiliated with

Also associated with

No associations

Rating

The Pressure Function for Products of Non-negative Matrices does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with The Pressure Function for Products of Non-negative Matrices, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and The Pressure Function for Products of Non-negative Matrices will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-232350