On the (Dis)connection between growth and primitive periodic points
Abstract
Abstract In 1972, Cornalba and Shiffman showed that the number of zeros of an order zero holomorphic function in two or more variables can grow arbitrarily fast. We generalize this finding to the setting of complex dynamics, establishing that the number of isolated primitive periodic points of an order zero holomorphic function in two or more variables can grow arbitrarily fast as well. This answers a recent question posed by Buhovsky et al.
Fields of Study & Subjects
Mathematical Dynamics and Fractals
Holomorphic and Operator Theory
Meromorphic and Entire Functions
Publication details
- Journal / source
- Bulletin of the London Mathematical Society
- Volume
- 58
- Issue
- 1
- Publication date
- 1 January 2026
- Language
- EN