Continued Fractions and the Transfer Operator Approach

The transfer operator approach is a concept first introduced by David Ruelle, a Belgian-French mathematical physicist, who worked on statistical physics and dynamical systems. He introduced the transfer operator a means to study dynamical zeta functions. A good introduction to chaotic systems, motivating and introducing dynamical zeta functions (in a general setting) is the web book. Our goal in this chapter is more specific. We focus solely on variants of the Artin billiard and the Mayer’s transfer operator approach. Surprisingly, the period functions, as defined in § 5.1 of the previous chapter, play a significant role in Mayer’s transfer operator theory.