Fatou components and singularities of meromorphic functions
We prove several results concerning the relative position of points in the postsingular set $P(f)$ of a meromorphic map $f$ and the boundary of a Baker domain or the successive iterates of a wandering component. For Baker domains we answer a question of Mihaljevi\'c-Brandt and Rempe-Gillen. For wand...
| Authors: | ; ; ; |
|---|---|
| Format: | Article |
| Status: | Accepted version |
| Publication date: | 2020 |
| Country: | España |
| Institution: | Universidad de Barcelona |
| Repository: | Dipòsit Digital de la UB |
| OAI Identifier: | oai:diposit.ub.edu:2445/130195 |
| Online Access: | https://hdl.handle.net/2445/130195 |
| Access Level: | Open access |
| Keyword: | Equacions funcionals Funcions analítiques Sistemes dinàmics complexos Polinomis Funcions enteres Funcions meromorfes Functional equations Analytic functions Complex dynamical systems Polynomials Entire functions Meromorphic functions |
| _version_ | 1878734418513756160 |
|---|---|
| author | Baranski, Krzysztof |
| author2 | Fagella Rabionet, Núria Jarque i Ribera, Xavier Karpinska, Boguslawa |
| author2_role | author author author |
| author_browse | Baranski, Krzysztof Fagella Rabionet, Núria Jarque i Ribera, Xavier Karpinska, Boguslawa |
| author_facet | Baranski, Krzysztof Fagella Rabionet, Núria Jarque i Ribera, Xavier Karpinska, Boguslawa |
| author_role | author |
| collection | Dipòsit Digital de la UB |
| description | We prove several results concerning the relative position of points in the postsingular set $P(f)$ of a meromorphic map $f$ and the boundary of a Baker domain or the successive iterates of a wandering component. For Baker domains we answer a question of Mihaljevi\'c-Brandt and Rempe-Gillen. For wandering domains we show that if the iterates $U_n$ of such a domain have uniformly bounded diameter, then there exists a sequence of postsingular values $p_n$ such that $\dist(p_n, U_n)\to 0$ as $n\to \infty$. We also prove that if $U_n \cap P(f)=\emptyset$ and the postsingular set of $f$ lies at a positive distance from the Julia set (in $\C$), then the sequence of iterates of any wandering domain must contain arbitrarily large disks. This allows to exclude the existence of wandering domains for some meromorphic maps with infinitely many poles and unbounded set of singular values. |
| eu_rights_str_mv | openAccess |
| format | article |
| id | ES_699d019d15bbcddb3fcf3fd2ecb8d2d7 |
| institution | Universidad de Barcelona |
| instname_str | Universidad de Barcelona |
| network_acronym_str | ES |
| network_name_str | España |
| oai_identifier_str | oai:diposit.ub.edu:2445/130195 |
| publishDate | 2020 |
| publishDateSort | 2020 |
| publisher | Cambridge University Press |
| publisherStr | Cambridge University Press |
| reponame_str | Dipòsit Digital de la UB |
| spelling | Fatou components and singularities of meromorphic functions Baranski, Krzysztof Fagella Rabionet, Núria Jarque i Ribera, Xavier Karpinska, Boguslawa Equacions funcionals Funcions analítiques Sistemes dinàmics complexos Polinomis Funcions enteres Funcions meromorfes Functional equations Analytic functions Complex dynamical systems Polynomials Entire functions Meromorphic functions We prove several results concerning the relative position of points in the postsingular set $P(f)$ of a meromorphic map $f$ and the boundary of a Baker domain or the successive iterates of a wandering component. For Baker domains we answer a question of Mihaljevi\'c-Brandt and Rempe-Gillen. For wandering domains we show that if the iterates $U_n$ of such a domain have uniformly bounded diameter, then there exists a sequence of postsingular values $p_n$ such that $\dist(p_n, U_n)\to 0$ as $n\to \infty$. We also prove that if $U_n \cap P(f)=\emptyset$ and the postsingular set of $f$ lies at a positive distance from the Julia set (in $\C$), then the sequence of iterates of any wandering domain must contain arbitrarily large disks. This allows to exclude the existence of wandering domains for some meromorphic maps with infinitely many poles and unbounded set of singular values. Cambridge University Press https://hdl.handle.net/2445/130195 |
| spellingShingle | Fatou components and singularities of meromorphic functions Baranski, Krzysztof Equacions funcionals Funcions analítiques Sistemes dinàmics complexos Polinomis Funcions enteres Funcions meromorfes Functional equations Analytic functions Complex dynamical systems Polynomials Entire functions Meromorphic functions |
| status_str | acceptedVersion |
| title | Fatou components and singularities of meromorphic functions |
| title_full | Fatou components and singularities of meromorphic functions |
| title_fullStr | Fatou components and singularities of meromorphic functions |
| title_full_unstemmed | Fatou components and singularities of meromorphic functions |
| title_short | Fatou components and singularities of meromorphic functions |
| title_sort | Fatou components and singularities of meromorphic functions |
| topic | Equacions funcionals Funcions analítiques Sistemes dinàmics complexos Polinomis Funcions enteres Funcions meromorfes Functional equations Analytic functions Complex dynamical systems Polynomials Entire functions Meromorphic functions |
| topic_facet | Equacions funcionals Funcions analítiques Sistemes dinàmics complexos Polinomis Funcions enteres Funcions meromorfes Functional equations Analytic functions Complex dynamical systems Polynomials Entire functions Meromorphic functions |
| url | https://hdl.handle.net/2445/130195 |