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In this article we study holomorphic integrals on tropical plane curves in view of ultradiscretization.
Fay, J. Theta functions on Riemann surfaces
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Mikhalkin, G. “Enumerative tropical algebraic geometry in R 2 R^{2} .” J, Amer. Math. Soc
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Einsiedler, M. Kapranov, M. and Lind, D. “Non-Archimedean amoebas and tropical varieties” J. Reine Angew. Math
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Inoue, R. and Takenawa, T. “Tropical spectral curves and integrable cellular automata.” Int. Math. Res. Not
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Kajiwara, K., Nobe, A. and Tsuda, T. “Ultradiscretization of solvable one-dimensional chaotic maps.” J. Phys. A Math. Theor
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Cited alongside, same era.
Helm, D. and Katz, E. ”Monodromy Filtrations and the Topology of Tropical Varieties.” arXiv/math.AG/08043651
Cited in the paper.
Mikhalkin, G. and Zharkov, I. “Tropical curves, their Jacobians and theta functions.” arXiv/math.AG/0612267
Cited in the paper.
Speyer, D. and Strumfels, B. “Tropical Mathematics.” arXiv/math.CO/0408099
Cited in the paper.
Speyer, D. ”Uniformizing Tropical Curves I: Genus Zero and One.” arXiv/math.AG/07112677
Cited in the paper.
Viro, O. “Patchworking real algebraic varieties.” arXiv/math.AG/0611382
Cited in the paper.
Katz, E., Markwig, H. and Markwig, T. ”The j j -invariant of a plane tropical cubic” J. Algebra
2008
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Payne, S. ”Fibres of tropicalization.” Math. Z
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