On the (Dis)connection between growth and primitive periodic points

Adi Glücksam; Shira Tanny

doi:10.1112/blms.70287

On the (Dis)connection between growth and primitive periodic points

Adi Glücksam
, Shira Tanny^*

^*Corresponding author for this work

Einstein Institute of Mathematics

Research output: Contribution to journal › Article › peer-review

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.

Original language	English
Article number	e70287
Journal	Bulletin of the London Mathematical Society
Volume	58
Issue number	1
DOIs	https://doi.org/10.1112/blms.70287
State	Published - Jan 2026

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© 2026 The Author(s). Bulletin of the London Mathematical Society is copyright © London Mathematical Society.

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10.1112/blms.70287

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On the (Dis)connection between growth and primitive periodic points

Abstract

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