Mathematical Research Letters
Volume 21 (2014)
On the growth of local intersection multiplicities in holomorphic dynamics: a conjecture of Arnold
Pages: 713 – 731
We show by explicit example that local intersection multiplicities in holomorphic dynamical systems can grow arbitrarily fast, answering a question of Arnold. On the other hand, we provide results showing that such behavior is exceptional, and that typically local intersection multiplicities grow subexponentially.