2012/12/20 by W. J. Gignac, William Gignac, Gignac, William
Mathematics · Physics and Astronomy · #32B10 (Secondary) #37F99 (Primary) 14C17 #Algebraic Geometry (math.AG) #Complex Variables (math.CV) #Dynamical Systems (math.DS) #FOS: Mathematics #Geometry and complex manifolds #Mathematical Dynamics and Fractals #Quantum chaos and dynamical systems #math.AG #math.CV #math.DS #msc:14C17 #msc:32B10 #msc:37F99
paper · pdf · doi:10.48550/arxiv.1212.5272
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
openalex publication_date 2012/12/20 · arxiv created 2014/02/25 · arxiv updated 2014/02/26 · openalex created_date 2022/10/03 · openalex updated_date 2026/07/28
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.