Tropicalizations of affine varieties give interesting ways to sketch and study affine varieties, whose tools are astonishingly elementary at the algebraic level. Not only that, studying algebraic dynamics on varieties may give interesting pictures under tropicalizations, as worked by Spalding and Veselov, or Filip. In this talk, we will introduce some basicmost ideas of tropicalizations, and play with the Markov cubic surfaces $$X^2+Y^2+Z^2+XYZ=AX+BY+CZ+D,$$ where A, B, C, D are parameters, as an example of tropical study of algebraic dynamics. It turns out that we obtain a $(\infty,\infty,\infty)$-triangle group action on the hyperbolic plane as a model of dynamics of interest. 언어: Korean (possibly English, depending on the audience)