Academic Journal
the fatou and julia sets of multivalued analytic functions: The Fatou and Julia sets of multivalued analytical functions
| Title: | the fatou and julia sets of multivalued analytic functions: The Fatou and Julia sets of multivalued analytical functions |
|---|---|
| Authors: | P. A. Gumenuk |
| Source: | Siberian Mathematical Journal. 43(6):1047-1054 |
| Publisher Information: | Russian Academy of Sciences - RAS (Rossiĭskaya Akademiya Nauk - RAN), Siberian Branch (Sibirskoe Otdelenie), Sobolev Insitute of Mathematics (Institut Matematiki Im. S. L. Soboleva), Novosibirsk, 2002. |
| Publication Year: | 2002 |
| Subject Terms: | Fatou set, multivalued function, analytic relation, Julia set, Small divisors, rotation domains and linearization in holomorphic dynamics, Functional equations in the complex plane, iteration and composition of analytic functions of one complex variable, Normal functions of one complex variable, normal families, complex dynamics, Dynamical systems involving relations and correspondences in one complex variable, normal family |
| Description: | The author defines, in a natural way, the notions of an analytic relation and the Fatou and Julia sets of an analytic relation. The main result of the paper reads as follows: The Julia set of an analytic relation \(f\) coincides with the closure of the set of all repelling periodic points of \(f\) (in the case when \(f\) is defined on the entire Riemann sphere, \(f\) should not have fractional linear branches). This theorem generalizes the well-known fact for single-valued complex analytic functions. |
| Document Type: | Article |
| File Description: | application/xml |
| ISSN: | 0037-4466 |
| DOI: | 10.1023/a:1021117301173 |
| Access URL: | https://zbmath.org/1899826 https://link.springer.com/article/10.1023/A%3A1021117301173 |
| Accession Number: | edsair.dedup.wf.002..bb6083fbc59ec02aa1c3397f5827f33f |
| Database: | OpenAIRE |
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