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

## TL;DR

This paper classifies a family of birational maps of C^2 based on their algebraic entropy, analyzing degree growth patterns to understand their dynamical behavior.

## Contribution

It introduces a dynamical classification method for a 9-parametric family of birational maps using degree growth analysis, extending previous studies.

## Key findings

- Identified conditions for periodic, linear, quadratic, and exponential degree growth.
- Computed the dynamical degree for various parameter settings.
- Included known birational maps as special cases.

## 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.