Disclosure: On Meta at Mathematics Stack Exchange, I have asked whether an algebraic-dynamics tag should be created and made a synonym of the existing arithmetic-dynamics tag there, given the apparent overlap or lack of clear boundary between the two areas. (See https://math.meta.stackexchange.com/q/31109/118539.)

In checking the situation on Math Overflow, I have found 8 questions tagged algebraic-dynamics and 28 questions tagged arithmetic-dynamics. I wonder whether it would be helpful on MO to make one of the tags a synonym of the other. (If I understand correctly, tag synonyms are not symmetric, as one tag remains the primary tag.)

Note the following (also used in my answer to a Mathematics Stack Exchange question asking about algebraic dynamics):

From nLab:

In

algebraic dynamicsone typically studies discrete dynamical systems on algebraic varieties. Such a system is given by a regular endomorphism $D: X \to X$ of a variety $X$....

The case over number fields is also called arithmetic dynamics...

That said, note also that Joseph Silverman writes in the introduction to *The Arithmetic of Dynamical Systems*, Springer 2007:

There is no firm line between arithmetic dynamics and algebraic dynamics, and indeed much of the material in this book is quite algebraic.

algebraic-arithmetic-dynamics, or justalgebraic-dynamics, with tag info saying explicitly that both algebraic dynamics and arithmetic dynamics are concerned. $\endgroup$ – YCor Jan 8 '20 at 17:13arithmetic dynamicshas the connotation that the base field is not closed and the problems have to do with that fact.Algebraic dynamicssuggests working over an algebraically closed field like $\mathbb C$ and studying dynamics of endomorphisms of algebraic varieties. ... $\endgroup$ – Joe Silverman Jan 14 '20 at 17:47arithmetic(number theory),algebraic geometry, anddynamical systems. The first two are algebraic in nature, butalgebrais too broad, which is why I preferarithmetic dynamicstoalgebraic dynamics. The latter should be "algebraic geometry dynamics", but that's more words than most people want to use. As a practical matter, the MSC category 37P is "Arithmetic and non-Archimedean dynamical systems", which leads toarithmetic dynamicsbeing used more thanalgebraic dynamics. $\endgroup$ – Joe Silverman Jan 14 '20 at 17:53