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arXiv · 2608.18426

A Relative Variational Principle for Expanding Iterated Function Systems

Gregory Hemenway·Jason Tu
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Abstract

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.

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Gregory Hemenway, Jason Tu. 2026-08-19. A Relative Variational Principle for Expanding Iterated Function Systems. https://arxiv.org/abs/2608.18426

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