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of 277
pro vyhledávání: '"37F99"'
We characterize two classical types of conformality of a holomorphic self-map of the unit disk at a boundary point - existence of a finite angular derivative in the sense of Carath\'eodory and the weaker property of angle preservation - in terms of t
Externí odkaz:
http://arxiv.org/abs/2410.13965
Autor:
Kim, Kyounghee
Let $\{F_n, n\ge 8\}$ be a family of diffeomorphisms on real rational surfaces that are birationally equivalent to birational maps on $\mathbf{P}^2(\mathbb{R})$. In this article, we investigate the mapping classes of the diffeomorphisms $F_n, n\ge 8$
Externí odkaz:
http://arxiv.org/abs/2407.15075
Autor:
Cruz-Zamorano, Francisco J.
A complete characterization of parabolic self-maps of finite shift is given in terms of their Herglotz's representation. This improves a previous result due to Contreras, D\'iaz-Madrigal, and Pommerenke. We also derive some consequences for the rate
Externí odkaz:
http://arxiv.org/abs/2407.10664
Let $\Omega$ be a regular Koenigs domain in the complex plane $\mathbb{C}$. We prove that the Hardy number of $\Omega$ is greater or equal to $1/2$. That is, every holomorphic function in the unit disc $f \colon \mathbb{D} \to \Omega$ belongs to the
Externí odkaz:
http://arxiv.org/abs/2405.17621
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:
Kim, Kyounghee
In this article, we define the orbit data of birational maps of $\mathbf{P}^2(\mathbb{C})$ and show that the orbit data determine the dynamical degree by providing the minimal polynomials of the dynamical degree in terms of orbit data. Using this, we
Externí odkaz:
http://arxiv.org/abs/2312.17729
This work studies the Hardy number for the class of hyperbolic planar domains satisfying Abel's inclusion property, which are usually known as Koenigs domains. More explicitly, we prove that for all regular domains in the above class, the Hardy numbe
Externí odkaz:
http://arxiv.org/abs/2312.17101
A classical problem in Complex Dynamics on hyperbolic domains is to characterize the hyperbolic step of parabolic functions. This topic has been studied by several authors, leading to different results and providing characterizations that depend on t
Externí odkaz:
http://arxiv.org/abs/2309.00402
Autor:
Chen, Yi-Chiuan, Kawahira, Tomoki
For the quadratic family $f_{c}(z) = z^2+c$ with $c$ in a hyperbolic component of the Mandelbrot set, it is known that every point in the Julia set moves holomorphically. In this paper we give a uniform derivative estimate of such a motion when the p
Externí odkaz:
http://arxiv.org/abs/2304.11231
Autor:
Kim, Kyounghee
The induced action on the Picard group of a rational surface automorphism with positive entropy can be identified with an element of the Coxeter group associated to $E_n, n\ge 10$ diagram. It follows that the set of dynamical degrees of rational surf
Externí odkaz:
http://arxiv.org/abs/2211.09662