Zobrazeno 1 - 10
of 12
pro vyhledávání: '"Luka Boc Thaler"'
Publikováno v:
Analysis & PDE 16 (2023) 35-88
The classification of Fatou components for rational functions was concluded with Sullivan's proof of the No Wandering Domains Theorem in 1985. In 2016 it was shown, in joint work of the first and last author with Buff, Dujardin and Raissy, that wande
Externí odkaz:
http://arxiv.org/abs/1907.04140
Autor:
Luka Boc Thaler
Publikováno v:
International Journal of Mathematics. 33
This is a corrigendum to the authors paper [A reconstruction theorem for complex polynomials, Int. J. Math. 26(9) (2015) 1550073]. Here we present a completely rewritten and self-contained Sec. 4 of the aforementioned paper and provide the reader wit
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::a5adbd8f9ab7249792988cb49eed8137
https://doi.org/10.1142/s0129167x22920045
https://doi.org/10.1142/s0129167x22920045
Autor:
Luka Boc Thaler
Publikováno v:
Bulletin of the London Mathematical Society. 53:1663-1673
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:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::b1a0e06f975fe46ee05eb4efbe55ed92
https://doi.org/10.1112/blms.12518
https://doi.org/10.1112/blms.12518
Short $${\mathbb {C}}^2$$ ’s were constructed in [5] 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
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::cdf93209b69225dc86dd4e3ff325db41
http://hdl.handle.net/2108/286051
http://hdl.handle.net/2108/286051
Autor:
Luka Boc Thaler
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:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::46d9948b08972fa15a4053129fcd80d1
http://arxiv.org/abs/2004.05420
http://arxiv.org/abs/2004.05420
A 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
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::a82ee9dd01d45dec2a97d589535299a4
http://arxiv.org/abs/1907.07457
http://arxiv.org/abs/1907.07457
Autor:
Uroš Kuzman, Luka Boc Thaler
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:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::2f816f221ce9085cb10032443c615527
http://arxiv.org/abs/1902.04192
http://arxiv.org/abs/1902.04192
Autor:
Franc Forstneric, Luka Boc Thaler
Publikováno v:
Analysis & PDE. 9:2031-2050
We construct for every integer n > 1 a complex manifold of dimension n which is exhausted by an increasing sequence of biholomorphic images of ℂn (i.e., a long ℂn), but does not admit any nonconstant holomorphic or plurisubharmonic functions. Fur
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::92533042c6c3d79cf843d2cd47446d14
https://doi.org/10.2140/apde.2016.9.2031
https://doi.org/10.2140/apde.2016.9.2031
Autor:
Luka Boc Thaler
Publikováno v:
International Journal of Mathematics. 31:2050075
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:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::61e5932a998d8effad7e9edbaad89d48
https://doi.org/10.1142/s0129167x20500755
https://doi.org/10.1142/s0129167x20500755
Publikováno v:
Ergodic theory and dynamical systems, 35(5), 1380-1393. Cambridge University Press
We study invariant Fatou components for holomorphic endomorphisms in $\mathbb{P}^2$. In the recurrent case these components were classified by Sibony and the second author in 1995. In 2008 Ueda completed this classification by proving that it is not
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::c7ec7d26c3f8196cfa3b2324f14a096f