arXiv subjects

Seung uk Jang

Publications and source records attributed to Seung uk Jang.

2 recordsLinked to original sources

arXiv2025

Tropical Dynamics of Markov Surfaces

We discuss the algebraic dynamics on Markov cubics generated by Vieta involutions, in the tropicalized setting. 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 $(\infty,\infty,\infty)$-triangle reflection group on the hyperbolic plane. This understanding of the tropicalized algebraic dynamics produces some results on Markov cubics over non-archimedean fields, including the existence of the Fatou domain and finitude of orbits with rational points having prime power denominators.

math.DS↗

arXiv2024

Kummer Rigidity for Hyperkähler Automorphisms

We show that a holomorphic automorphism on a projective hyperkähler manifold that has positive topological entropy and has volume measure as the measure of maximal entropy, is necessarily a Kummer example, partially extending the analogous results in (Cantat-Dupont 2020)(Filip-Tosatti 2018) for complex surfaces. A trick with Jensen's inequality is used to show that stable and unstable distributions exhibit uniform rate of contraction and expansion, and with them our hyperkähler manifold is shown to be flat. A result in (Greb-Kebekus-Peternell 2016) then implies that our hyperkähler manifold is birational to a torus quotient, giving the Kummer example structure.

math.DS↗