The Pentagram Map is Recurrent
暂无分享,去创建一个
The pentagram map is defined on the space of convex n-gons (considered up to projective equivalence) by drawing the diagonals that join second-nearest-neighbors in an n-gon and taking the new n-gon formed by the intersections. We prove that th is map is recurrent; thus, for almost any starting polygon, repeated application of the pentagram map will show a near copy of the starting polygon appear infinitely often under various perspectives.
[1] D. Hilbert,et al. Geometry and the Imagination , 1953 .
[2] V. Arnold. Mathematical Methods of Classical Mechanics , 1974 .
[3] Richard Evan Schwartz,et al. The Pentagram Map , 1992, Exp. Math..
[4] F. Pirani. MATHEMATICAL METHODS OF CLASSICAL MECHANICS (Graduate Texts in Mathematics, 60) , 1982 .