On the degree growth of birational mappings in higher dimension
Copyright policy )On the degree growth of birational mappings in higher dimension
Let $f$ be a birational map of ${\bf C}^d$, and consider the degree complexity, or asymptotic degree growth rate $δ(f)=\lim_{n\to\infty}({\rm deg}(f^n))^{1/n}$. We introduce a family of elementary maps, which have the form $f=L\circ J$, where $L$ is (invertible) linear, and $J(x_1,...,x_d)=(x_1^{-1},...,x_d^{-1})$. We develop a method of regularization and show how it can be used to compute $δ$ for an elementary map.
- Indiana University Bloomington United States
- Indiana University United States
- Syracuse University United States
- DePaul University United States
dynamical degree, Mathematics - Complex Variables, Iteration of holomorphic maps, fixed points of holomorphic maps and related problems for several complex variables, Dynamical Systems (math.DS), birational mappings, Dynamics of complex polynomials, rational maps, entire and meromorphic functions; Fatou and Julia sets, 37F99 32H50 14E07, FOS: Mathematics, Mathematics - Dynamical Systems, Complex Variables (math.CV), Rational and birational maps
dynamical degree, Mathematics - Complex Variables, Iteration of holomorphic maps, fixed points of holomorphic maps and related problems for several complex variables, Dynamical Systems (math.DS), birational mappings, Dynamics of complex polynomials, rational maps, entire and meromorphic functions; Fatou and Julia sets, 37F99 32H50 14E07, FOS: Mathematics, Mathematics - Dynamical Systems, Complex Variables (math.CV), Rational and birational maps
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