Dynamical Zeta Functions and Dynamical Determinants for Hyperbolic Maps: A Functional Approach

The spectra of transfer operators associated to dynamical systems, when acting on suitable Banach spaces, contain key information about the ergodic properties of the systems. Focusing on expanding and hyperbolic maps, this book gives a self-contained account on the relation between zeroes of dynamical determinants, poles of dynamical zeta functions, and the discrete spectra of the transfer operators.

In the hyperbolic case, the first key step consists in constructing a suitable Banach space...