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pro vyhledávání: '"Osborne, J. W."'
In transcendental dynamics significant progress has been made by studying points whose iterates escape to infinity at least as fast as iterates of the maximum modulus. Here we take the novel approach of studying points whose iterates escape at least
Externí odkaz:
http://arxiv.org/abs/1609.06644
Autor:
Osborne, J. W., Sixsmith, D. J.
Publikováno v:
Aequationes mathematicae, 90, 5 (2016), 1025-1034
We study the class $\mathcal{M}$ of functions meromorphic outside a countable closed set of essential singularities. We show that if a function in $\mathcal{M}$, with at least one essential singularity, permutes with a non-constant rational map $g$,
Externí odkaz:
http://arxiv.org/abs/1603.07497
We investigate the connectedness properties of the set $ I^{\!+\!}(f) $ of points where the iterates of an entire function $ f $ are unbounded. In particular, we show that $ I^{\!+\!}(f) $ is connected whenever iterates of the minimum modulus of $ f
Externí odkaz:
http://arxiv.org/abs/1504.05611
Autor:
Osborne, J. W., Sixsmith, D. J.
Publikováno v:
Ann. Acad. Sci. Fenn. Math, 41, (2016), 561-578
For a transcendental entire function f, we study the set of points BU(f) whose iterates under f neither escape to infinity nor are bounded. We give new results on the connectedness properties of this set and show that, if U is a Fatou component that
Externí odkaz:
http://arxiv.org/abs/1503.08077
Autor:
Osborne, J. W.
We show that, if the Julia set of a transcendental entire function is locally connected, then it takes the form of a spider's web in the sense defined by Rippon and Stallard. In the opposite direction, we prove that a spider's web Julia set is always
Externí odkaz:
http://arxiv.org/abs/1110.3256
Autor:
Osborne, J. W.
Building on recent work by Rippon and Stallard, we explore the intricate structure of the spider's web fast escaping sets associated with certain transcendental entire functions. Our results are expressed in terms of the components of the complement
Externí odkaz:
http://arxiv.org/abs/1011.0359
Publikováno v:
Radiation Research, 1979 Oct 01. 80(1), 161-169.
Externí odkaz:
https://www.jstor.org/stable/3575122
Publikováno v:
Radiation Research, 1978 Oct 01. 76(1), 95-104.
Externí odkaz:
https://www.jstor.org/stable/3574930
Publikováno v:
Radiation Research, 1970 Jul 01. 43(1), 131-142.
Externí odkaz:
https://www.jstor.org/stable/3572864
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