题目：           Mathematical explanation of the phyllotaxis

报告人：      Andrei Lodkin (St. Petersburg State University)

时间地点：   2018.07.26  15:00pm  N205

摘要：           The regular spiral arrangement of various parts of biological objects (leaves, branches, florets, seeds, etc.), known as phyllotaxis, could not find an explanation during several centuries (Leonardo, Kepler, Goethe, . . . ). Some quantitative parameters of the phyllotaxis (the divergence angle being the principal one) show that the organization in question is, in a sense,the same in the large family of living objects, and the divergence angle is mainly close to the golden number. This was a mystery, and numerous explanations of this phenomenon remained \lyrical". Later, similar patterns were discovered in inorganic objects (L. Levitov, S. Douady & Y. Couder,et al). After a series of computer models, it was only in the XXI century that the rigorous explanation of the appearance of the golden number in a simple mathematical model has been given. The resulting pattern is related to stable fixed points of an operator acting on a finite-dimensional torus and depends on a real parameter. The variation of this parameter leads to an interesting bifurcation diagram (actually, a binary tree) where the limiting object (a kind of the boundary of the tree) is the SL(2; Z)-orbit of the golden number on the segment [0,1]