Some counterexamples in dynamics of rational semigroups

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dc.creatorStankewitz, Rich
dc.creatorSugawa, Toshiyuki
dc.creatorSumi, Hiroki
dc.date2007-08-25
dc.date.accessioned2026-07-07T08:25:44Z
dc.date.available2026-07-07T08:25:44Z
dc.descriptionWe give an example of two rational functions with non-equal Julia sets that generate a rational semigroup whose completely invariant Julia set is a closed line segment. We also give an example of polynomials with unequal Julia sets that generate a non nearly Abelian polynomial semigroup with the property that the Julia set of one generator is equal to the Julia set of the semigroup. These examples show that certain conjectures in the field of dynamics of rational semigroups do not hold as stated and therefore require the allowance of certain exceptional cases.
dc.description13 pages
dc.identifierhttps://arxiv.org/abs/0708.3434
dc.identifierhttp://arxiv.org/abs/0708.3434
dc.identifierAnn. Acad. Sci. Fenn. Math. 29 (2004), no. 2, 357--366
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/136720
dc.subjectDynamical Systems
dc.subjectComplex Variables
dc.subject37F10 (Primary) 37F50, 30D05 (Secondary)
dc.titleSome counterexamples in dynamics of rational semigroups
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