Planar tropical caustics: trivalency and convexity

Tropical caustic of a convex domain on the plane is a canonically associated tropical analytic curve inside the domain. In this note we give a graphical proof for the classification of its intermediate vertices, implying in particular that they are always trivalent. Apart from that we explain how various known examples of tropical caustics are constructed and discuss the posibility of relaxing the convexity conditionon for the domain.

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Journal
Serdica Mathematical Journal
Published
2025-10-14
DOI
https://doi.org/10.55630/serdica.2025.51.47-72
Primary Topic
Coastal and Marine Dynamics
Type
article
Field-Weighted Citation Impact
0.00

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article

Planar tropical caustics: trivalency and convexity

Mikhail Shkolnikov
Serdica Mathematical Journal
Coastal and Marine Dynamics
article

Planar tropical caustics: trivalency and convexity

Mikhail Shkolnikov
article en

Abstract

Tropical caustic of a convex domain on the plane is a canonically associated tropical analytic curve inside the domain. In this note we give a graphical proof for the classification of its intermediate vertices, implying in particular that they are always trivalent. Apart from that we explain how various known examples of tropical caustics are constructed and discuss the posibility of relaxing the convexity conditionon for the domain.

Serdica Mathematical JournalVol. 51(1)
Institute of Mathematics and Informatics (BG)
Science Foundation Ireland
Openalex Percentile: Top 69%
Coastal and Marine Dynamics
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