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http://hdl.handle.net/2445/164138
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DC Field | Value | Language |
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dc.contributor.author | Fagella Rabionet, Núria | - |
dc.contributor.author | Garijo, Antonio | - |
dc.date.accessioned | 2020-06-03T09:32:18Z | - |
dc.date.available | 2020-06-03T09:32:18Z | - |
dc.date.issued | 2007-05-31 | - |
dc.identifier.issn | 0010-3616 | - |
dc.identifier.uri | http://hdl.handle.net/2445/164138 | - |
dc.description.abstract | We consider the families of entire transcendental maps given by $F_{\lambda, m}(\mathrm{z})=\lambda \mathrm{z}^{m} \exp (\mathrm{z}),$ where $m \geq 2 .$ All functions $F_{\lambda, m}$ have a superattracting fixed point at $z=0,$ and a critical point at z $=-m .$ In the parameter planes we focus on the capture zones, i.e., $\lambda$ values for which the critical point belongs to the basin of attraction of $\mathrm{z}=0,$ denoted by $A(\mathrm{o}) .$ In particular, we study the main capture zone (parameter values for which the critical point lies in the immediate basin, $A^{*}(\mathrm{o})$ ) and prove that is bounded, connected and simply connected. All other capture zones are unbounded and simply connected. For each parameter $\lambda$ in the main capture zone, $A(o)$ consists of a single connected component with non-locally connected boundary. For all remaining values of $\lambda, A^{*}$ (o) is a quasidisk. On a different approach, we introduce some families of holomorphic maps of $\mathbb{C}^{*}$ which serve as a model for $F_{\lambda, m},$ in the sense that they are related by means of quasiconformal surgery to $F_{\lambda, m}$. | - |
dc.format.extent | 29 p. | - |
dc.format.mimetype | application/pdf | - |
dc.language.iso | eng | - |
dc.publisher | Springer Verlag | - |
dc.relation.isformatof | Versió postprint del document publicat a: https://doi.org/10.1007/s00220-007-0265-8 | - |
dc.relation.ispartof | Communications in Mathematical Physics, 2007, vol. 273, num. 3, p. 755-783 | - |
dc.relation.uri | https://doi.org/10.1007/s00220-007-0265-8 | - |
dc.rights | (c) Springer Verlag, 2007 | - |
dc.source | Articles publicats en revistes (Matemàtiques i Informàtica) | - |
dc.subject.classification | Funcions enteres | - |
dc.subject.classification | Sistemes dinàmics complexos | - |
dc.subject.other | Entire functions | - |
dc.subject.other | Complex dynamical systems | - |
dc.title | The Parameter Planes of $\lambda \mathrm{z}^{m} \exp (\mathrm{z})$ for $m \geq 2^{*}$ | - |
dc.type | info:eu-repo/semantics/article | - |
dc.type | info:eu-repo/semantics/acceptedVersion | - |
dc.identifier.idgrec | 550482 | - |
dc.date.updated | 2020-06-03T09:32:18Z | - |
dc.rights.accessRights | info:eu-repo/semantics/openAccess | - |
Appears in Collections: | Articles publicats en revistes (Matemàtiques i Informàtica) |
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File | Description | Size | Format | |
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550482.pdf | 676.3 kB | Adobe PDF | View/Open |
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