Probabilistic approximation of partly filled-in composite Julia sets

• We study properties of the metric space of pluriregular sets and of contractions on that space induced by finite families of proper polynomial mappings of several complex variables. In particular, we show that closed balls in the space of pluriregular sets do not have to be compact and we give a simple proof of applicability of the so-called chaos game in the case of composite Julia sets. Part of the construction of those sets also leads to a computationally viable approximation by simpler sets based on Monte-Carlo simulation.

Subject headings

NATURVETENSKAP  -- Matematik (hsv//swe)

NATURAL SCIENCES  -- Mathematics (hsv//eng)

Keyword

composite Julia sets

pluricomplex Green functions

iterated function system

the chaos game

complex dynamics

Monte-Carlo simulation

Publication and Content Type

ref (subject category)

art (subject category)