The projective heat map
Author(s)
Bibliographic Information
The projective heat map
（Mathematical surveys and monographs, v. 219）
American Mathematical Society, c2017
Available at / 28 libraries
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Library, Research Institute for Mathematical Sciences, Kyoto University数研
S||MSM||219200037074200
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Note
Includes bibliographical references (p. 193-195)
Description and Table of Contents
Description
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.
Table of Contents
Introduction
Part 1: Some other polygon iterations
A primer on projective geometry
Elementary algebraic geometry
The pentagram map
Some related dynamical systems
Part 2: The projective heat map
Topological degree of the map
The convex case
The basic domains
The method of positive dominance
The Cantor set
Towards the quasi horseshoe
The quasi horseshoe
Part 3: Sketches for the remaining results
Towards the solenoid
The solenoid
Local structure of the Julia set
The embedded graph
Connectedness of the Julia set
Terms, formulas, and coordinate listings
References
by "Nielsen BookData"
