Golden and Silver Stationary Points in Probe Particle Dynamics within a Modular Domain

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 equila...

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Bibliographic Details
Published in:Functional analysis and its applications 2024-06, Vol.58 (2), p.129-142
Main Authors: Gorsky, Alexander, Nechaev, Sergei
Format: Article
Language:English
Subjects:
14/34
639/766/189
639/766/530
639/766/747
Analysis
Functional Analysis
Group dynamics
Mathematics
Mathematics and Statistics
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Summary: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.
ISSN:0016-2663
1573-8485
DOI:10.1134/S0016266324020047