Zobrazeno 1 - 10
of 48
pro vyhledávání: '"Rippon, Philip J."'
Autor:
Benini, Anna Miriam, Evdoridou, Vasiliki, Fagella, Núria, Rippon, Philip J., Stallard, Gwyneth M.
We prove sharp results about recurrent behaviour of orbits of forward compositions of inner functions, inspired by fundamental results about iterates of inner functions, and give examples to illustrate behaviours that cannot occur in the simpler case
Externí odkaz:
http://arxiv.org/abs/2405.11866
Autor:
Benini, Anna Miriam, Evdoridou, Vasiliki, Fagella, Núria, Rippon, Philip J., Stallard, Gwyneth M.
There are many classical results, related to the Denjoy--Wolff Theorem, concerning the relationship between orbits of interior points and orbits of boundary points under iterates of holomorphic self-maps of the unit disc. Here, for the first time, we
Externí odkaz:
http://arxiv.org/abs/2203.06235
Autor:
Benini, Anna Miriam, Evdoridou, Vasiliki, Fagella, Núria, Rippon, Philip J., Stallard, Gwyneth M.
Publikováno v:
In Advances in Mathematics June 2024 446
For a transcendental entire function $f$, the property that there exists $r>0$ such that $m^n(r)\to\infty$ as $n\to\infty$, where $m(r)=\min \{|f(z)|:|z|=r\}$, is related to conjectures of Eremenko and of Baker, for both of which order $1/2$ minimal
Externí odkaz:
http://arxiv.org/abs/2102.02158
Although detailed descriptions of the possible types of behaviour inside periodic Fatou components have been known for over 100 years, a classification of wandering domains has only recently been given. Recently, simply connected wandering domains we
Externí odkaz:
http://arxiv.org/abs/2011.14736
We give a general method for constructing examples of transcendental entire functions of given small order, which allows precise control over the size and shape of the set where the minimum modulus of the function is relatively large. Our method invo
Externí odkaz:
http://arxiv.org/abs/2011.09532
Autor:
Benini, Anna Miriam, Evdoridou, Vasiliki, Fagella, Núria, Rippon, Philip J., Stallard, Gwyneth M.
While the dynamics of transcendental entire functions in periodic Fatou components and in multiply connected wandering domains are well understood, the dynamics in simply connected wandering domains have so far eluded classification. We give a detail
Externí odkaz:
http://arxiv.org/abs/1910.04802
We show that for many families of transcendental entire functions $f$ the property that $m^n(r)\to\infty$ as $n\to \infty$, for some $r>0$, where $m(r)=\min\{|f(z)|:|z|=r\}$, implies that the escaping set $I(f)$ of $f$ has the structure of a spider's
Externí odkaz:
http://arxiv.org/abs/1810.07814
Publikováno v:
Ann. Acad. Sci. Fenn. Math. 42, 2 (2017), 859-873
In 1970 G. R. MacLane asked if it is possible for a locally univalent function in the class $\mathcal{A}$ to have an arc tract. This question remains open, but several results about it have been given. We significantly strengthen these results, in pa
Externí odkaz:
http://arxiv.org/abs/1611.03292
Let $f$ and $g$ be permutable transcendental entire functions. We use a recent analysis of the dynamical behaviour in multiply connected wandering domains to make progress on the long standing conjecture that the Julia sets of $f$ and $g$ are equal;
Externí odkaz:
http://arxiv.org/abs/1503.08112