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Wiman–Valiron Discs and the Dimension of Julia Sets
- Source :
- International Mathematics Research Notices. 2021:9545-9566
- Publication Year :
- 2020
- Publisher :
- Oxford University Press (OUP), 2020.
-
Abstract
- We show that the Hausdorff dimension of the set of points of bounded orbit in the Julia set of a meromorphic map with a simply connected direct tract and a certain restriction on the singular values is strictly greater than one. This result is obtained by proving new results related to Wiman–Valiron theory.
- Subjects :
- Mathematics::Complex Variables
General Mathematics
010102 general mathematics
Dimension (graph theory)
01 natural sciences
Julia set
010101 applied mathematics
Combinatorics
Singular value
Bounded function
Hausdorff dimension
Simply connected space
0101 mathematics
Orbit (control theory)
Mathematics
Meromorphic function
Subjects
Details
- ISSN :
- 16870247 and 10737928
- Volume :
- 2021
- Database :
- OpenAIRE
- Journal :
- International Mathematics Research Notices
- Accession number :
- edsair.doi.dedup.....298985fc3e4e05d07cda995a41552f95