Pseudorandom Numbers for Conformal Measure

TL;DR

This paper introduces a novel algorithm for generating pseudorandom numbers that approximate conformal measures for continuous maps, demonstrating effectiveness on hyperbolic rational functions and their Julia sets.

Contribution

The paper presents a new algorithm for pseudorandom number generation of conformal measures, applicable to hyperbolic rational maps and their Julia sets.

Findings

Algorithm provides accurate approximations of generic points.

Effective for hyperbolic rational functions of degree two.

Works with potential related to Hausdorff dimension.

Abstract

We propose a new algorithm for generating pseudorandom (pseudo-generic) numbers of conformal measures of a continuous map T acting on a compact space X and for a Holder continuous potential F. In particular, we show that this algorithm provides good approximations to generic points for hyperbolic rational functions of degree two and the potential -h log|T'|, where h denotes the Hausdorff dimension of the Julia set of T .