Books & Math

A collection of books lying about the house that make me happy:

• Le Ton beau de Marot: Hofstadter
• Eugene Onegin: Pushkin/Hofstadter
• Einstein's Dreams: Lightman
• Reunion: Lightman
• Letters to a Young Poet: Rilke
• Perfume: Suskind
• Buddhism Plain & Simple: Hagen
• Little Book of Wisdom: The Dalai Lama
• Fundamentals of Musical Composition: Schoenberg
• Nexus: Buchanan
• Ubiquity - Why Catastrophes Happen: Buchanan
• Chaos - An Introduction to Dynamical Systems: Alligood, Sauer, & Yorke

I just opened up this last one to a random page: first a definiton of Lyapunov Exponents, then the 2D Brouwer Fixed Point Theorem, and finally a definition of a chaotic orbit. I love this book for many reasons, especially how the authors explain Li and Yorke's result from their paper "Period Three Implies Chaos": in a "challenge" exercise the reader is gently guided through 10 steps resulting in a proof of Sharkovskii's Theorem, an even more general result. And here is a definition of Chaos itself.

Here is a nifty little site with great explanations and, most importantly, pictures of chaos-related concepts:

• Introduction
• Bifurcation
• Sensitive Dependence on Initial Conditions