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The Projective Heat Map

About this Title

Richard Evan Schwartz, Brown University, Providence, RI

Publication: Mathematical Surveys and Monographs
Publication Year: 2017; Volume 219
ISBNs: 978-1-4704-3514-1 (print); 978-1-4704-4050-3 (online)
DOI: https://doi.org/10.1090/surv/219
MathSciNet review: MR3642552
MSC: Primary 37-02; Secondary 14E05, 26A18, 37B05, 37E30, 51M15

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Table of Contents

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Front/Back Matter

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Chapters

• 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