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Funktsional'nyi Analiz i ego Prilozheniya, 2024, Volume 58, Issue 2, Pages 34–51
DOI: https://doi.org/10.4213/faa4187 (Mi faa4187) 		 
Golden and silver stationary points in probe particle dynamics within a modular domain

Aleksandr Gorskyab, Sergei Nechaevcdb

a Institute for Information Transmission Problems of the Russian Academy of Sciences (Kharkevich Institute), Moscow, Russia
b Center for Neurophysics and Neuromorphic Technologies, Complex Networks Laboratory, Moscow, Russia
c Laboratoire de Physique Théorique et Modèles Statistiques, Centre National de la Recherche Scientifique, Paris, France
d Université Paris-Saclay, Paris, France
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DOI: https://doi.org/10.4213/faa4187
Abstract: 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, phyllotaxis.
Received: 08.12.2023
Revised: 17.12.2023
Accepted: 24.12.2023
Published: 30.04.2024
English version:
Functional Analysis and Its Applications, 2024, Volume 58, Issue 2, Pages 129–142
DOI: https://doi.org/10.1134/S0016266324020047
Bibliographic databases:
Document Type: Article
MSC: 06Cxx, 11B39, 11F20
Language: Russian
Citation: Aleksandr Gorsky, Sergei Nechaev, “Golden and silver stationary points in probe particle dynamics within a modular domain”, Funktsional. Anal. i Prilozhen., 58:2 (2024), 34–51; Funct. Anal. Appl., 58:2 (2024), 129–142
Citation in format AMSBIB
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