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pro vyhledávání: '"Hlushchanka, Mikhail"'
We consider rational maps $f$ on the Riemann sphere $\widehat {\mathbb{C}}$ with an $f$-invariant set $P\subset \widehat {\mathbb{C}}$ of four marked points containing the postcritical set of $f$. We show that the dynamics of the corresponding Thurst
Externí odkaz:
http://arxiv.org/abs/2411.00732
An orientation-preserving branched covering map $f\colon S^2 \to S^2$ is called a critically fixed Thurston map if $f$ fixes each of its critical points. It was recently shown that there is an explicit one-to-one correspondence between M\"obius conju
Externí odkaz:
http://arxiv.org/abs/2212.14759
We provide a natural canonical decomposition of postcritically finite rational maps with non-empty Fatou sets based on the topological structure of their Julia sets. The building blocks of this decomposition are maps where all Fatou components are Jo
Externí odkaz:
http://arxiv.org/abs/2209.02800
Every Thurston map $f\colon S^2\rightarrow S^2$ on a $2$-sphere $S^2$ induces a pull-back operation on Jordan curves $\alpha\subset S^2\setminus P_f$, where $P_f$ is the postcritical set of $f$. Here the isotopy class $[f^{-1}(\alpha)]$ (relative to
Externí odkaz:
http://arxiv.org/abs/2105.06938
Autor:
Geyer, Lukas, Hlushchanka, Mikhail
We provide a complete combinatorial classification of critically fixed anti-Thurston maps, i.e., orientation-reversing branched covers of the 2-sphere that fix every critical point. The first step in the proof, and an interesting result in its own ri
Externí odkaz:
http://arxiv.org/abs/2006.10788
Akademický článek
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Autor:
Hlushchanka, Mikhail
A rational map $f:\widehat{\mathbb{C}}\to\widehat{\mathbb{C}}$ on the Riemann sphere $\widehat{\mathbb{C}}$ is called critically fixed if each critical point of $f$ is fixed under $f$. In this article we study properties of a combinatorial invariant,
Externí odkaz:
http://arxiv.org/abs/1904.04759
Autor:
Hlushchanka, Mikhail, Meyer, Daniel
Iterated monodromy groups of postcritically-finite rational maps form a rich class of self-similar groups with interesting properties. There are examples of such groups that have intermediate growth, as well as examples that have exponential growth.
Externí odkaz:
http://arxiv.org/abs/1610.02814
Autor:
Hlushchanka, Mikhail, Meyer, Daniel
Publikováno v:
Proceedings of the London Mathematical Society, 116(6), 1489. Oxford University Press
Proceedings of the London Mathematical Society
PROCEEDINGS OF THE LONDON MATHEMATICAL SOCIETY
Proceedings of the London Mathematical Society
PROCEEDINGS OF THE LONDON MATHEMATICAL SOCIETY
Iterated monodromy groups of postcritically-finite rational maps form a rich class of self-similar groups with interesting properties. There are examples of such groups that have intermediate growth, as well as examples that have exponential growth.
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::a090431684f942cd5c18df09a4b58d72
https://dspace.library.uu.nl/handle/1874/410832
https://dspace.library.uu.nl/handle/1874/410832