TL;DR
This paper investigates how the dynamics of certain complex maps on tori and toric varieties lead to the natural emergence of tropical objects in the limit, connecting complex dynamics with tropical geometry.
Contribution
It introduces a framework for understanding the tropicalization of dynamical systems on complex tori and toric varieties, highlighting new links between complex dynamics and tropical geometry.
Findings
Tropical objects appear naturally in the limit of dynamical systems on complex tori.
Several theorems in tropical geometry are reviewed in the context of dynamical systems.
The analysis reveals a deep connection between complex dynamics and tropical geometry.
Abstract
We analyse the dynamics of the pullback of the map on the complex tori and toric varieties. We will observe that tropical objects naturally appear in the limit, and review several theorems in tropical geometry.
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Taxonomy
TopicsAdvanced Differential Equations and Dynamical Systems · Advanced Combinatorial Mathematics