Symbolic Open Systems

Using the full power of countable alphabet thermodynamic formalism and modern functional analysis laid down in Volume 1, the second volume of the book presents a systematic treatment of the perturbative approach to symbolic open dynamical systems, covering those generated by a large class of naturally occurring holes through which the dynamical medium escapes. It highlights bounded mean oscillation Keller Banach spaces, surviving eigenvalues of perturbed Perron-Frobenius operators and their peripheral spectrum, along with corresponding eigenfunctions and eigenmeasures, escape rates, conditionally invariant measures, and surviving equilibrium states. This volume extensively addresses the issue when holes approach a given hole.