On the (Dis)connection Between Growth and Primitive Periodic Points
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 L. Buhovsky, I. Polterovich, L. Polterovich, E. Shelukhin and V. Stojisavljevi\'c.
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