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Full Description
This book is on the celebrated topic of rational billiards, translation surfaces and their fractal analogs. It contains a gentle introduction to Complec analysis and Complex geometry on Riemann surfaces. The book also touches on the topic of moduli spaces of translation surfaces and the SL2R action thereon. The author then discusses his own research in fractal billiards. This book is suitable for advanced undergraduates and beginning graduate students looking to get into the field of rational billiards and translations surfaces (and their generalizations, e.g., flows on moduli spaces of translation surfaces).
Contents
Background. Necessary background (complex analysis on surfaces, etc.). Billiard dynamics. Fractal geometry (for later understanding fractal billiard examples). Rational billiards. Translation surfaces from rational billiards. A complex analytic approach to constructing a translation surface. Commenting Chapter 2-4, the Veech dichotomy and other classic results on squaretiled billiard tables. Fractal billiards.
