Seung uk Jang, Vieta Involutions on Tropical Markov Cubics

We discuss the algebraic dynamics on Markov cubics generated by Vieta involutions, in the tropicalized setting, including some introduction to the tropicalization. It turns out that there is an invariant subset of the tropicalized Markov cubic where the action by Vieta involutions can be modeled by that of the Farey reflection group on the hyperbolic plane.

Some applications in non-archimedean dynamics, number theory, or complex dynamical questions will also be introduced.