Pseudorandom Numbers for Conformal Measure

2009/05/06 by Manfred Denker, Denker, Manfred, Jinqiao Duan +3
Mathematics · #37A50 #37F10 #37F15 #60H15 #86A05 #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Analysis and Transform Methods #Mathematical Dynamics and Fractals #Numerical Analysis (math.NA) #advanced mathematical theories

paper · pdf · doi:10.48550/arxiv.0905.0729

openalex publication_date 2009/05/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 .

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