On the set where the iterates of an entire function are neither escaping nor bounded
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چکیده
منابع مشابه
Connectedness properties of the set where the iterates of an entire function are bounded
We investigate some connectedness properties of the set of points K(f) where the iterates of an entire function f are bounded. We describe a class of transcendental entire functions for which K(f) is totally disconnected if and only if each component of K(f) containing a critical point is aperiodic. Moreover we show that, for such functions, if K(f) is disconnected then it has uncountably many ...
متن کاملThe Open University ’ s repository of research publications and other research outputs Connectedness properties of the set where the iterates of an entire function are bounded
We investigate some connectedness properties of the set of points K(f) where the iterates of an entire function f are bounded. We describe a class of transcendental entire functions for which K(f) is totally disconnected if and only if each component of K(f) containing a critical point is aperiodic. Moreover we show that, for such functions, if K(f) is disconnected then it has uncountably many ...
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We investigate some connectedness properties of the set of points K(f) where the iterates of an entire function f are bounded. We describe a class of transcendental entire functions for which K(f) is totally disconnected if and only if each component of K(f) containing a critical point is aperiodic. Moreover we show that, for such functions, if K(f) is disconnected then it has uncountably many ...
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ژورنال
عنوان ژورنال: Annales Academiae Scientiarum Fennicae Mathematica
سال: 2016
ISSN: 1239-629X,1798-2383
DOI: 10.5186/aasfm.2016.4134