RUS  ENG
Full version
JOURNALS // Funktsional'nyi Analiz i ego Prilozheniya

Funktsional. Anal. i Prilozhen., 2024, Volume 58, Issue 2, Pages 34–51 (Mi faa4187)

Golden and silver stationary points in probe particle dynamics within a modular domain
Aleksandr Gorsky, Sergei Nechaev

References

1. F. Rothen, A.-J. Koch, “Phyllotaxis, or the properties of spiral lattices. I. Shape invariance under compression”, J. Physique, 50:6 (1989), 633–657  crossref  mathscinet
2. F. Rothen, A.-J. Koch, “Phyllotaxis or the properties of spiral lattices. II. Packing of circles along logarithmic spirals”, J. Physique, 50:13 (1989), 1603–1621  crossref  mathscinet
3. M. Kunz, F. Rothen, “Phyllotaxis or the properties of spiral lattices. III. An algebraic model of morphogenesis”, J. Physique I, 2:11 (1992), 2131–2172  crossref  adsnasa
4. Hyun-Woo Lee, L. S. Levitov, “Universality in phyllotaxis: a mechanical theory”, Symmetry in plants, Ser. Math. Biol. Med., 4, World Sci. Publ., Singapore, 1998, 619–653  crossref  zmath
5. V. W. de Spinadel, “The metallic means family and multifractal spectra”, Nonlinear Anal., 36, Ser. B: Real World Appl.:6 (1999), 721–745  crossref  mathscinet  zmath
6. K. Itô, H. P. McKean, Jr., Diffusion processes and their sample paths, Classics Math., Reprint of the 1974 ed., Springer-Verlag, Berlin, 1996, xv+323 pp.  crossref  mathscinet  zmath  zmath
7. E. Helfand, D. S. Pearson, “Statistics of the entanglement of polymers: unentangled loops and primitive paths”, J. Chem. Phys., 79:4 (1983), 2054–2059  crossref  adsnasa
8. S. K. Nechaev, “Topological properties of a two-dimensional polymer chain in the lattice of obstacles”, J. Phys. A, 21:18 (1988), 3659–3671  crossref  mathscinet  zmath  adsnasa
9. S. Nechaev, K. Polovnikov, “From geometric optics to plants: the eikonal equation for buckling”, Soft Matter, 13:7 (2017), 1420–1429  crossref  adsnasa
10. R. Rammal, G. Toulouse, M. A. Virasoro, “Ultrametricity for physicists”, Rev. Modern Phys., 58:3 (1986), 765–788  crossref  mathscinet  adsnasa
11. L. S. Levitov, “Energetic approach to phyllotaxis”, Europhys. Lett., 14:6 (1991), 533–539  crossref  adsnasa
12. M. Livio, The golden ratio. The story of phi, the world's most astonishing number, Reprint of 2002 ed., Broadway Books, New York, 2008, x+294 pp.  mathscinet  zmath
13. O. R. Musin, A. S. Tarasov, “The Tammes problem for $N=14$”, Exp. Math., 24:4 (2015), 460–468  crossref  mathscinet  zmath
14. E. L. Altschuler, T. J. Williams, E. R. Ratner, R. Tipton, R. Stong, F. Dowla, F. Wooten, “Possible global minimum lattice configurations for Thomson's problem of charges on a sphere”, Phys. Rev. Lett., 78:14 (1997), 2681–2685  crossref  adsnasa
15. A. A. Abrikosov, “The magnetic properties of superconducting alloys”, J. Phys. Chem. Solids, 2:3 (1957), 199–208  crossref  adsnasa
16. A. Flack, A. Gorsky, S. Nechaev, “Generalized Devil's staircase and RG flows”, Nuclear Phys. B, 996 (2023), 116376, 44 pp.  crossref  mathscinet  zmath  adsnasa
17. C. O'Sullivan, “Formulas for non-holomorphic Eisenstein series and for the Riemann zeta function at odd integers”, Res. Number Theory, 4:3 (2018), 36, 38 pp.  crossref  mathscinet  zmath
18. P. Ribeiro, S. Yakubovich, “On the Epstein zeta function and the zeros of a class of Dirichlet series”, J. Math. Anal. Appl., 530:1 (2024), 127590  crossref  mathscinet  zmath
19. C. L. Siegel, Lectures on advanced analytic number theory, Notes by S. Raghavan, Tata Inst. Fundam. Res. Lect. Math., 23, Tata Inst. Fund. Res., Bombay, 1965, iii+331+iii pp.  mathscinet  zmath
20. Y. Motohashi, “A new proof of the limit formula of Kronecker”, Proc. Japan Acad., 44:7 (1968), 614–616  crossref  mathscinet  zmath
21. L. S. Levitov, “Phyllotaxis of flux lattices in layered superconductors”, Phys. Rev. Lett., 66:2 (1991), 224–227  crossref  mathscinet  zmath  adsnasa
22. S. Gukov, “RG flows and bifurcations”, Nuclear Phys. B, 919 (2017), 583–638  crossref  mathscinet  zmath  adsnasa
23. A. Flack, S. Nechaev, BKT in phyllotaxis, arXiv: 2310.05580
24. T. Koshy, Fibonacci and Lucas numbers with applications, v. 2, Pure Appl. Math. (Hoboken), John Wiley & Sons, Inc., Hoboken, NJ, 2019, xviii+729 pp.  crossref  mathscinet  zmath
25. A. P. Akande, R. Schneider, “Semi-modular forms from Fibonacci–Eisenstein series”, Ramanujan J., 60:1 (2023), 59–68  crossref  mathscinet  zmath
26. E. Gorsky, A. Oblomkov, J. Rasmussen, V. Shende, “Torus knots and the rational DAHA”, Duke Math. J., 163:14 (2014), 2709–2794  crossref  mathscinet  zmath
27. K. Taşköprü, I. Altintaş, “HOMFLY polynomials of torus links as generalized Fibonacci polynomials”, Electron. J. Combin., 22:4 (2015), 4.8, 17 pp.  crossref  mathscinet  zmath


© Steklov Math. Inst. of RAS, 2026