A Relative Variational Principle for Expanding Iterated Function Systems

The variational principle is a key tool in the study of invariant measures for chaotic dynamical systems. In recent times, dynamicists have developed techniques in random and nonstationary systems to better model real-world phenomena. Here, we prove a relative variational principle for a class of expanding iterated function systems. In particular, we use a nonstationary Ruelle–Perron–Frobenius theorem to show that the marginal entropy given an ergodic invariant measure on the symbolic base equals the average topological entropy along fibers in the induced skew product.