|
|
|
|
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 |
| 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 |
| 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 |
| 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 |
| 5. |
V. W. de Spinadel, “The metallic means family and multifractal spectra”, Nonlinear Anal., 36, Ser. B: Real World Appl.:6 (1999), 721–745 |
| 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. |
| 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 |
| 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 |
| 9. |
S. Nechaev, K. Polovnikov, “From geometric optics to plants: the eikonal equation for buckling”, Soft Matter, 13:7 (2017), 1420–1429 |
| 10. |
R. Rammal, G. Toulouse, M. A. Virasoro, “Ultrametricity for physicists”, Rev. Modern Phys., 58:3 (1986), 765–788 |
| 11. |
L. S. Levitov, “Energetic approach to phyllotaxis”, Europhys. Lett., 14:6 (1991), 533–539 |
| 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. |
| 13. |
O. R. Musin, A. S. Tarasov, “The Tammes problem for $N=14$”, Exp. Math., 24:4 (2015), 460–468 |
| 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 |
| 15. |
A. A. Abrikosov, “The magnetic properties of superconducting alloys”, J. Phys. Chem. Solids, 2:3 (1957), 199–208 |
| 16. |
A. Flack, A. Gorsky, S. Nechaev, “Generalized Devil's staircase and RG flows”, Nuclear Phys. B, 996 (2023), 116376, 44 pp. |
| 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. |
| 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 |
| 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. |
| 20. |
Y. Motohashi, “A new proof of the limit formula of Kronecker”, Proc. Japan Acad., 44:7 (1968), 614–616 |
| 21. |
L. S. Levitov, “Phyllotaxis of flux lattices in layered superconductors”, Phys. Rev. Lett., 66:2 (1991), 224–227 |
| 22. |
S. Gukov, “RG flows and bifurcations”, Nuclear Phys. B, 919 (2017), 583–638 |
| 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. |
| 25. |
A. P. Akande, R. Schneider, “Semi-modular forms from Fibonacci–Eisenstein series”, Ramanujan J., 60:1 (2023), 59–68 |
| 26. |
E. Gorsky, A. Oblomkov, J. Rasmussen, V. Shende, “Torus knots and the rational DAHA”, Duke Math. J., 163:14 (2014), 2709–2794 |
| 27. |
K. Taşköprü, I. Altintaş, “HOMFLY polynomials of torus links as generalized Fibonacci polynomials”, Electron. J. Combin., 22:4 (2015), 4.8, 17 pp. |