Extremal F-Exponents of Finitely Irreducible CGDMSs: a math dissertation research talk.

An in person chalkboard version of this talk was presented at the University of North Texas's Dynamical Systems Seminar in person on April 19th, 2024.

Abstract: Given a Hölder family of functions 𝐹 and a finitely irreducible CGDMS Φ encoded by a symbolic representation 𝐸∞𝐴, one may associate to each coding 𝜔∈𝐸∞𝐴 a Birkhoff average 𝜉(𝜔) called the 𝐹-exponent of 𝜔, should it exist. The ergodic optimization of these exponents by way of zero-temperature style limits is important to the characterization of Birkhoff spectra for CGDMSs. In this talk, we will introduce the objects at play in this optimization problem and the results which address this problem for a large collection of possible families 𝐹.

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This talk is related to my recent preprint on multifractal analysis of finitely irreducible conformal graph directed Markov systems, this work is a portion of my upcoming dissertation that I am completing under the direction of my PhD advisor Dr. Mariusz Urbański.

You can find my preprint on ResearchGate here: https://www.researchgate.net/publicat...

It is also available on the arXiv here: https://arxiv.org/abs/2404.09348