Geodesic
Golden and silver stationary points in probe particle dynamics within a modular domain
Funkcionalʹnyj analiz i ego priloženiâ, Tome 58 (2024) no. 2, pp. 34-51 Cet article a éte moissonné depuis la source Math-Net.Ru

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The flows generated by the iterative dynamics of triangle reflections are analyzed. These flows are interpreted as the adiabatic dynamics of probe particles within the fundamental domain of the modular group. Two specific cases of lattices are considered: (a) those generated by reflections of equilateral triangles, and (b) those generated by reflections of rectangular isosceles triangles. We demonstrate that the stationary points of the flows for equilateral and isosceles triangles correspond to the “Golden” and the “Silver” ratios, respectively.
Keywords: golden and silver ratios, modular group, euclidean plane tiling, elliptic functions, adiabatic dynamics
Mots-clés : phyllotaxis. 
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Aleksandr Gorsky; Sergei Nechaev. Golden and silver stationary points in probe particle dynamics within a modular domain. Funkcionalʹnyj analiz i ego priloženiâ, Tome 58 (2024) no. 2, pp. 34-51. http://geodesic.mathdoc.fr/item/FAA_2024_58_2_a3/

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