Mathematical Research Letters

Volume 21 (2014)

Number 4

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

Pages: 713 – 731

DOI: http://dx.doi.org/10.4310/MRL.2014.v21.n4.a7

Author

William Gignac (School of Mathematics, Georgia Institute of Technology, Atlanta, Georgia, U.S.A.)

Abstract

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.

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