2016/02/08 by Le, Quang-Nhat · 1 citation
#26C15 #32H50 #37C80 #37E99 #51N15 #Algebraic Geometry (math.AG) #Dynamical Systems (math.DS) #FOS: Mathematics
paper · doi:10.48550/arxiv.1602.02699
The pentagram map was invented by Richard Schwartz in his search for a projective-geometric analogue of the midpoint map. It turns out that the dynamical behavior of the pentagram map is totally different from that of the midpoint map. Recently, Schwartz has constructed a related map, the projective heat map, which empirically exhibits similar dynamics as the midpoint map. In this paper, we will demonstrate that there is a one-parameter family of maps which behaves a lot like Schwartz's projective heat map.