arXiv subjects

Jonathan M Fraser

Publications and source records attributed to Jonathan M Fraser.

2 recordsLinked to original sources

arXiv2025

Dimensions of orbital sets in complex dynamics

Let $ E $ be a non-empty compact subset of the Riemann sphere and $T$ be a rational map of degree at least two. We study the associated \emph{orbital set}, that is, the backwards orbit of $E$ under $T$, and study the relationship between the upper box dimension of the orbital set and the upper box dimensions of the Julia set of $T$ and the initial set $ E$. Our results extend previous work on inhomogeneous iterated function systems to the setting of complex dynamical systems.

math.DS↗

arXiv2022

Parabolic carpets

We introduce and study a family of non-conformal and non-uniformly contracting iterated function systems. We refer to the attractors of such systems as parabolic carpets. Roughly speaking they may be thought of as nonlinear analogues of self-affine carpets which are allowed to have parabolic fixed points. We compute the $L^q$-spectrum of a class of weak Gibbs measures supported on parabolic carpets as well as the box dimensions of the carpet itself.

math.DS↗