Equilibrium Stability for Open Zooming Systems

Abstract

We prove that for a wide family of open zooming systems and zooming potentials we have equilibrium stability, i.e., the equilibrium states depend continuously on the dynamics and the potential. We consider the open zooming systems with special holes and quite general contractions and zooming potentials with locally Hölder induced potential, which include the Hölder ones. We also prove stability for skew-products with the base being a zooming system like above. As a consequence of finiteness and stability, we obtain uniqueness of equilibrium state.

We added a proof of uniqueness from finiteness and stability. Comments are welcome! arXiv admin note: substantial text overlap with arXiv:2010.08143