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- W3046565035 abstract "Let $f$ be a function in the Eremenko-Lyubich class $mathcal{B}$, and let $U$ be an unbounded, forward invariant Fatou component of $f$. We relate the number of singularities of an inner function associated to $f|_U$ with the number of tracts of $f$. In particular, we show that if $f$ lies in either of two large classes of functions in $mathcal{B}$, and also has finitely many tracts, then the number of singularities of an associated inner function is at most equal to the number of tracts of $f$. Our results imply that for hyperbolic functions of finite order there is an upper bound -- related to the order -- on the number of singularities of an associated inner function." @default.
- W3046565035 created "2020-08-07" @default.
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- W3046565035 date "2018-07-19" @default.
- W3046565035 modified "2023-09-27" @default.
- W3046565035 title "Singularities of inner functions associated with hyperbolic maps" @default.
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