Dynamical Classification of a Family of Birational Maps of C^2 via Algebraic Entropy

Abstract

This work dynamically classifies a 9-parametric family of birational maps f : C2 -> C2. From the sequence of the degrees dn of the iterates of f, we find the dynamical degree delta(f) of f. We identify when dn grows periodically, linearly, quadratically or exponentially. The considered family includes the birational maps studied by Bedford and Kim in [4] as one of its subfamilies.

arXiv admin note: text overlap with arXiv:1702.00959

References in corpus (4)

• The Dynamical Degrees of a Mapping
• Non-autonomous 2-periodic Gumovski-Mira difference equations
• Invariant Fibrations for some Birational Maps of C^2
• Zero Entropy for Some Birational Maps of C^2