arXiv subjects

Gregory Hemenway

Publications and source records attributed to Gregory Hemenway.

4 recordsLinked to original sources

arXiv2026

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.

math.DS↗

arXiv2026

A Nonstationary Ruelle-Perron-Frobenius Theorem

The Ruelle-Perron-Frobenius theorem is a powerful tool in the study of equilibrium measures and their statistical properties. We prove a nonstationary version of this theorem under general conditions involving an invariant sequence of real convex cones in function space.

math.DS↗

arXiv2025

Conjugacies of Expanding Skew Products on $\mathbb{T}^n$

We show that any equilibrium state for a Hölder potential on the model map $\vec{x} \mapsto d \cdot \vec{x} \mod \mathbb{Z}^n$ on $\mathbb{T}^n$ is conjugate to Lebesgue measure for an invariant expanding skew product of degree $d$. This is a generalization of a result of McMullen to higher dimensions for equilibrium states. We use an approach developed by the author using a family of nonstationary transfer operators for an expanding skew product. We also apply a Markov partition argument to classify invariant probability measures for expanding maps on $\mathbb{T}^n$.

math.DS↗

arXiv2023

Equilibrium States for Non-Uniformly Expanding Skew Products

We study equilibrium states for non-uniformly expanding skew products, and show how a family of fiberwise transfer operators can be used to define the conditional measures along fibers of the product. We prove that the pushforward of the equilibrium state onto the base of the product is itself an equilibrium state for a Hölder potential defined via these fiberwise transfer operators.

math.DS↗