References for the Advanced Calculus 2 lectures

In this note we list the bibliographic references for the Advanced Calculus 2 lectures given by Ricardo A. Sáenz at UNM, on Tuesday and Thursday, April 18 and 20.

Most of the material of the lectures can be found in the book Mathematics of Fractals, by Masaya Yamaguti, Masayoshi Hata and Jun Kigami, published by the AMS (1997). There you can find the proof of the existence and uniqueness of self-similar sets given a finite collection of contractions, and the proof of Hutchinson’s theorem.

Hutchinson’s theorem was proved by John E. Hutchinson and published in the paper “Fractals and self-similarity”, Indiana Univ. Math. Journal 30 (1981), pp. 713-747. You can find it in his webpage: Research Papers.

The fractal made of golden rectangles was published by Marc Frantz in the paper “A Fractal Made of Golden Sets”, Mathematics Magazine 82 (2009), pp. 243-254. You can find the paper in JSTOR: A Fractal Made of Golden Sets.

The Hausdorff dimension was published by Felix Hausdorff in the paper “Dimension und äußeres Maß” (Dimension and Outer Measure) in Mathematische Annalen 79 (1918), pp. 157-179. You can find the paper in the European Digital Mathematics Library: Dimension und äußeres Maß.