Zobrazeno 1 - 10
of 60
pro vyhledávání: '"Evdoridou, Vasiliki"'
This paper is concerned with universality properties of composition operators $C_f$, where the symbol $f$ is given by a transcendental entire function restricted to parts of its Fatou set. We determine universality of $C_f$ when $f$ is restricted to
Externí odkaz:
http://arxiv.org/abs/2409.16260
One of the fundamental distinctions in McMullen and Sullivan's description of the Teichm\"uller space of a complex dynamical system is between discrete and indiscrete grand orbit relations. We investigate these on the Fatou set of transcendental enti
Externí odkaz:
http://arxiv.org/abs/2405.15667
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
We introduce a new approximation technique into the context of complex dynamics that allows us to construct examples of transcendental entire functions with unbounded wandering domains. We provide examples of entire functions with an orbit of unbound
Externí odkaz:
http://arxiv.org/abs/2210.13350
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
The set of points where an entire function achieves its maximum modulus is known as the maximum modulus set. In 1951, Hayman studied the structure of this set near the origin. Following work of Blumenthal, he showed that, near zero, the maximum modul
Externí odkaz:
http://arxiv.org/abs/2012.07409
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
Publikováno v:
Arnold Mathematical Journal 6 (2020), 459-493
Suppose that $f$ is a transcendental entire function, $V \subsetneq \mathbb{C}$ is a simply connected domain, and $U$ is a connected component of $f^{-1}(V)$. Using Riemann maps, we associate the map $f \colon U \to V$ to an inner function $g \colon
Externí odkaz:
http://arxiv.org/abs/2002.03320
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