On the growth of local intersection multiplicities in holomorphic dynamics: a conjecture of Arnold

Abstract

We show by explicit example that local intersection multiplicities in holomorphic dynamical systems can grow arbitrarily fast, answering a question of V. I. Arnold. On the other hand, we provide results showing that such behavior is exceptional, and that typically local intersection multiplicities grow subexponentially.

13 pages. In version 2, we've included an alternate, more geometric construction of the counterexample to Arnold's conjecture. We've also added new theorems illustrating that Arnold's conjecture holds "generically." To appear in Math. Res. Lett