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pro vyhledávání: '"Thaler, Luka Boc"'
Autor:
Astorg, Matthieu, Thaler, Luka Boc
We study the local dynamics of generic skew-products tangent to the identity, i.e. maps of the form $P(z,w)=(p(z), q(z,w))$ with $dP_0=\mathrm{id}$. More precisely, we focus on maps with non-degenerate second differential at the origin; such maps hav
Externí odkaz:
http://arxiv.org/abs/2204.02644
Autor:
Thaler, Luka Boc
We study the geometry of simply connected wandering domains for entire functions and we prove that every bounded connected regular open set, whose closure has a connected complement, is a wandering domain of some entire function. In particular such d
Externí odkaz:
http://arxiv.org/abs/2012.13284
Autor:
Thaler, Luka Boc
We prove that the Euclidean ball can be realized as a Fatou component of a holomorphic automorphism of $\mathbb{C}^m$, in particular as the escaping and the oscillating wandering domain. Moreover, the same is true for a large class of bounded domains
Externí odkaz:
http://arxiv.org/abs/2004.05420
Autor:
Thaler, Luka Boc
We introduce a new class of entire functions $\mathcal{E}$ which consists of all $F_0\in\mathcal{O}(\mathbb{C})$ for which there exists a sequence $(F_n)\in \mathcal{O}(\mathbb{C})$ and a sequence $(\lambda_n)\in\mathbb{C}$ satisfying $F_n(z)=\lambda
Externí odkaz:
http://arxiv.org/abs/1908.06026
A {\sl parabolic cylinder} is an invariant, non-recurrent Fatou component $\Omega$ of an automorphism $F$ of $\mathbb C^2$ satisfying: (1) The closure of the $\omega$-limit set of $F$ on $\Omega$ contains an isolated fixed point, (2) there exists a u
Externí odkaz:
http://arxiv.org/abs/1907.07457
Autor:
Thaler, Luka Boc, Kuzman, Uroš
Publikováno v:
Ergod. Th. Dynam. Sys. 41 (2021) 1612-1626
We consider the dynamics of complex rational maps on the Riemann sphere. We prove that, after reducing their orbits to a fixed number of positive values representing the Fubini-Study distances between finitely many initial elements of the orbit and t
Externí odkaz:
http://arxiv.org/abs/1902.04192
Short $\mathbb{C}^2$'s were constructed in [F] as attracting basins of a sequence of holomorphic automorphisms whose rate of attraction increases superexponentially. The goal of this paper is to show that such domains also arise naturally as autonomo
Externí odkaz:
http://arxiv.org/abs/1901.07394
Autor:
Thaler, Luka Boc, Forstneric, Franc
Publikováno v:
Anal. PDE 9 (2016) 2031-2050
In this paper we construct for every integer $n>1$ a complex manifold of dimension $n$ which is exhausted by an increasing sequence of biholomorphic images of $\mathbb C^n$ (i.e., a long $\mathbb C^n$), but it does not admit any nonconstant holomorph
Externí odkaz:
http://arxiv.org/abs/1511.05075
Autor:
Thaler, Luka Boc
Recently Takens' Reconstruction Theorem was studied in the complex analytic setting by Forn{\ae}ss and Peters \cite{FP}. They studied the real orbits of complex polynomials, and proved that for non-exceptional polynomials ergodic properties such as m
Externí odkaz:
http://arxiv.org/abs/1502.00233
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