Real topological entropy versus metric entropy for birational measure-preserving transformations
The authors consider the one-parameter family of maps \(F_\alpha :\mathbb{C}^2\to\mathbb{C}^2\) of the form \[ (x,z)\mapsto \left(y-1-\alpha,x\;\frac{y-\alpha}{y+1}\right). \] They discuss the growth rate of periodic points (here called entropy), the corresponding zetafunction and the Arnold complexity for two-dimensional maps (counting the number of complex intersections of a given line). Real versions of the notions are introduced by counting only periodic points which are real. The major part of the paper describes numerical simulations mainly on Lyapunov exponents.
scientific article; zbMATH DE number 1538270
scientific article