On the Degree Growth of Birational Mappings in Higher Dimension

2004/06/30 by Eric Bedford, Bedford, Eric, Kyounghee Kim +1 · 3 citations
Mathematics · #37F99 32H50 14E07 #Complex Variables (math.CV) #Dynamical Systems (math.DS) #FOS: Mathematics #math.CV #math.DS #msc:14E07 #msc:32H50 #msc:37F99

paper · pdf · doi:10.48550/arxiv.math/0406621

arxiv created 2004/08/16 · arxiv updated 2009/12/01

Abstract

Let f be a birational map of \bf C^d, and consider the degree complexity, or asymptotic degree growth rate δ(f)=lim_n→∞(\rm deg(fⁿ))^1/n. We introduce a family of elementary maps, which have the form f=L∘ J, where L is (invertible) linear, and J(x₁,...,x_d)=(x₁^-1,...,x_d^-1). We develop a method of regularization and show how it can be used to compute δ for an elementary map.

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