Zobrazeno 1 - 10
of 32
pro vyhledávání: '"Sixsmith, D. J."'
Autor:
Pardo-Simón, L., Sixsmith, D. J.
We study the maximum modulus set, $\mathcal{M}(p)$, of a polynomial $p$. We are interested in constructing $p$ so that $\mathcal{M}(p)$ has certain exceptional features. Jassim and London gave a cubic polynomial $p$ such that $\mathcal{M}(p)$ has one
Externí odkaz:
http://arxiv.org/abs/2007.07529
Autor:
Pardo-Simón, L., Sixsmith, D. J.
In 1909, Hardy gave an example of a transcendental entire function, $f$, with the property that the set of points where $f$ achieves its maximum modulus, $\mathcal{M}(f)$, has infinitely many discontinuities. This is one of only two known examples of
Externí odkaz:
http://arxiv.org/abs/1911.05408
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
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:
Sixsmith, D. J.
Publikováno v:
Ergod. Th. Dynam. Sys. 36 (2016) 2273-2292
We study the iteration of functions in the exponential family. We construct a number of sets, consisting of points which escape to infinity `slowly', and which have Hausdorff dimension equal to 1. We prove these results by using the idea of an annula
Externí odkaz:
http://arxiv.org/abs/1407.4638
Autor:
Sixsmith, D. J.
Publikováno v:
Math. Proc. Camb. Phil. Soc. 158 (2015) 365-383
We partition the fast escaping set of a transcendental entire function into two subsets, the maximally fast escaping set and the non-maximally fast escaping set. These sets are shown to have strong dynamical properties. We show that the intersection
Externí odkaz:
http://arxiv.org/abs/1403.7362
Autor:
Sixsmith, D. J.
Publikováno v:
Proc. Amer. Math. Soc. 143, 6 (2015), 2597-2612
We study a family of transcendental entire functions of genus zero, for which all of the zeros lie within a closed sector strictly smaller than a half-plane. In general these functions lie outside the Eremenko-Lyubich class. We show that for function
Externí odkaz:
http://arxiv.org/abs/1311.6987
Autor:
Sixsmith, D. J.
Publikováno v:
International Mathematics Research Notices 2015, 19 (2015), 9751-9774
We study the dynamics of a collection of families of transcendental entire functions which generalises the well-known exponential and cosine families. We show that for functions in many of these families the Julia set, the escaping set and the fast e
Externí odkaz:
http://arxiv.org/abs/1309.3099
Autor:
Sixsmith, D. J.
Publikováno v:
J. Anal. Math. 123 (2014), 95-105
The Eremenko-Lyubich class of transcendental entire functions with a bounded set of singular values has been much studied. We give a new characterisation of this class of functions. We also give a new result regarding direct singularities which are n
Externí odkaz:
http://arxiv.org/abs/1205.1976
Autor:
Sixsmith, D. J.
Publikováno v:
Pure Appl. Math. Q. 8, 4 (2012), 1029-1046
We give an example of a transcendental entire function with a simply connected fast escaping Fatou component, but with no multiply connected Fatou components. We also give a new criterion for points to be in the fast escaping set.
Externí odkaz:
http://arxiv.org/abs/1201.1926