This book introduces a simple dynamical model for a planar heat map
that is invariant under projective transformations. The map is
defined by iterating a polygon map, where one starts with a finite
planar $N$-gon and produces a new $N$-gon by a prescribed geometric
construction. One of the appeals of the topic of this book is the
simplicity of the construction that yet leads to deep and far
reaching mathematics. To construct the projective heat map, the
author modifies the classical affine invariant midpoint map, which
takes a polygon to a new polygon whose vertices are the midpoints
of the original. The author provides useful background which makes
this book accessible to a beginning graduate student or advanced
undergraduate as well as researchers approaching this subject from
other fields of specialty. The book includes many illustrations,
and there is also a companion computer program.
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