1. The Flapping Birds in the Pentagram Zoo
- Author
-
Schwartz, Richard Evan
- Subjects
Mathematics - Dynamical Systems ,Mathematics - Combinatorics - Abstract
We study the $(k+1,k)$ diagonal map for $k=2,3,4,...$. We call this map $\Delta_k$. The map $\Delta_1$ is the pentagram map and $\Delta_k$ is a generalization. $\Delta_k$ does not preserve convexity, but we prove that $\Delta_k$ preserves a subset $B_k$ of certain star-shaped polygons which we call $k$-birds. The action of $\Delta_k$ on $B_k$ seems similar to the action of $\Delta_1$ on the space of convex polygons. We show that some classic geometric results about $\Delta_1$ generalize to this setting., Comment: 60 pages, computer experiment inspired but mostly traditional math
- Published
- 2024