Gibbs Variational Principle and Fredholm Theory for One-Dimensional Maps

Abstract

In the present paper the following formal power series associated with a 1-dim map F plays an important role:

$${D_\beta}(z)=\exp\left[{-\Sigma{z^n}{Q_n}\left(\beta\right)/n}\right],{Q_n}\left(\beta\right)=\sum\limits_{{F^n}t=t}{}|\left({{F^n}}\right)'\left(t\right){|^{-\beta}}$$

((1))

where Fⁿt=F(F(…(F(t))…)) (n times).