An in person chalkboard version of this talk was presented at Dynamical Systems and Fractal Geometry Conference that was hosted at the University of North Texas May 14-17th, 2024. This talk was given on the 16th.
We organized this conference in part to honor the lifetime achievement of my PhD Advisor Dr. Mariusz Urbański who was awarded the Sierpiński medal for his contribution to his areas of research in mathematics. His laureate Wacław Sierpiński lecture was titled: Operatory Ruella i miary konforemne z zastosowaniami w teorii liczb i geometrii fraktalnej (Ruelle operators and conformal measures with applications to number theory and fractal geometry). As I mention in the video, it has been my great joy to pursue my dissertation research under the mentorship of Dr. Urbański and I would not be the mathematician I am today without him.
Abstract: We will take a moment to recall a result from Fan et al. (2009) regarding a characterization of the Khintchine spectrum of the Gauss map. Proceeding by analogy, we then define multifractal decompositions with respect to F-exponents and state a general result that applies to a wider class of systems and spectra. Our brief dive into multifractal analysis ends with a look at an example of the Lyapunov spectrum for a particular Lüroth
expansion.
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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: www.researchgate.net/publicat...
It is also available on the arXiv here: arxiv.org/abs/2404.09348
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I have given another talk concerning this paper on a different subject and documented it here: • Extremal F-Exponents o...
30 май 2024
