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• W2963669488 abstract "We investigate the dynamics ofsemigroups generated by a family of polynomial maps on the Riemann spheresuch that the postcritical set in the complex plane is bounded.The Julia set of such a semigroup may not be connected in general.We show that for such apolynomial semigroup,if $A$ and $B$ are two connected components of the Julia set,then one of $A$ and $B$ surrounds the other. From this,it is shown that each connected component of the Fatou set iseither simply or doubly connected.Moreover, we show that the Julia set of such a semigroupis uniformly perfect.An upper estimate of the cardinality of the set of allconnected components of the Julia set of such a semigroup is given.By using this, we givea criterion for the Julia setto be connected.Moreover, we show that for any $nin N cup { aleph _{0}} ,$there exists a finitely generated polynomial semigroup with boundedplanar postcritical setsuch that the cardinality of the set of all connected components of theJulia set is equal to $n.$Many new phenomena of polynomial semigroups that do not occur in the usual dynamics of polynomialsare found and systematically investigated." @default.
• W2963669488 created "2019-07-30" @default.
• W2963669488 creator A5087163683 @default.
• W2963669488 date "2011-01-01" @default.
• W2963669488 modified "2023-09-26" @default.
• W2963669488 title "Dynamics of postcritically bounded polynomial semigroups I: Connected components of the Julia sets" @default.
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• W2963669488 doi "https://doi.org/10.3934/dcds.2011.29.1205" @default.
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