Is it a good idea to create a tag called "algebraic-dynamics" and make it a tag synonym for arithmetic-dynamics?
Note that the current text (good for a quick impression, but probably needs expanding) for the arithmetic dynamics tag is:
Arithmetic dynamics combines the study of dynamical systems with number theory.
See this question on what is algebraic dynamics. In my answer to it, I note that Silverman writes that there is no firm line between arithmetic dynamics and algebraic dynamics in his The Arithmetic of Dynamical Systems, Springer 2007. [emphasis mine]