On the growth of local intersection multiplicities in holomorphic   dynamics: a conjecture of Arnold
  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. 
William Gignac
math.DS math.AG math.CV