The Flapping Birds in the Pentagram Zoo

Richard Evan Schwartz

We study the $(k+1,k)$ diagonal map for $k=2,3,4,...$. We call this map $\hat{I}{”}_k$. The map $\hat{I}{”}_1$ is the pentagram map and $\hat{I}{”}_k$ is a generalization. $\hat{I}{”}_k$ does not preserve convexi…