Dimension theory for infinite-alphabet conformal iterated function system limit sets

Abstract: Studying the extremely delicate geometric-measure-theoretic properties of dynamical limit sets is often an endeavor beset with myriad challenges. In this vein, we focus on the dimension-theoretic study of continued fraction Cantor sets -- a rich seam inaugurated by the work of Jarník and Besicovitch in the 1920s. I will report on two projects about such fascinating fractals. The first considers small perturbations of a conformal iterated function system (CIFS); while the second resolves two recent questions posed by Chousionis, Leykekhman, and Urbański regarding the dimension spectrum of a CIFS (i.e. the set of all Hausdorff dimensions of its various subsystem limit sets). We hope to present several interesting problems and directions that await resolution and explorations by the brilliant Bremen dynamics group 🙂

dynamical systems

Audience: researchers in the topic

Bremen Online Dynamics Seminar

Series comments: Talks are approx. 55 min plus discussion. Talks are not recorded.

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