Zero Entropy for Some Birational Maps of C^2

Abstract

This work deals with a special case of family of birational maps f : C2 -> C2 dynamically classified in [9]. In this work we study the zero entropy sub families of f. The sequence of degrees dn associated to the iterates of f is found to grow periodically, linearly, quadratically or exponentially. Explicit invariant fibrations for zero entropy families and all the integrable and periodic mappings inside the family f are given.

References in corpus (3)

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

Cited by in corpus (1)

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