Dynamics of postcritically bounded polynomial semigroups

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dc.creatorSumi, Hiroki
dc.date2007-03-20
dc.date2007-11-26
dc.date.accessioned2026-07-07T08:44:43Z
dc.date.available2026-07-07T08:44:43Z
dc.descriptionWe investigate the dynamics of semigroups generated by a family of polynomial maps on the Riemann sphere such that the postcritical set in the complex plane is bounded. Moreover, we investigate the associated random dynamics of polynomials. We show that for such a polynomial semigroup, if $A$ and $B$ are two connected components of the Julia set, then one of $A$ and $B$ surrounds the other. Moreover, we show that for any $n\in \Bbb{N} \cup \{\aleph_{0}\} ,$ there exists a finitely generated polynomial semigroup with bounded planar postcritical set such that the cardinality of the set of all connected components of the Julia set is equal to $n.$ Furthermore, we show that under a certain condition, a random Julia set is almost surely a Jordan curve, but not a quasicircle. Many new phenomena of polynomial semigroups and random dynamics of polynomials that do not occur in the usual dynamics of polynomials are found and systematically investigated.
dc.description2 figures. Lemma 4.31 and Lemma 4.37 are updated. See also http://www.math.sci.osaka-u.ac.jp/~sumi/welcomeou-e.html
dc.identifierhttps://arxiv.org/abs/math/0703591
dc.identifierhttp://arxiv.org/abs/math/0703591
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/142760
dc.subjectDynamical Systems
dc.subjectComplex Variables
dc.subjectProbability
dc.subject37F10; 37H10
dc.titleDynamics of postcritically bounded polynomial semigroups
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