Welington de Melo - Selected Works

Welington de Melo (Guap, 1946 - Rio de Janeiro, 2016) was a brazilian mathematician whose contributions were deeply connected with Smale and Palis school of dynamical systems. In particular the classification of smooth dynamical systems and the study of its generic properties are recurrent topics in his work. This book collected some of his most significant contributions, from his early work on structural stability of diffeomorphisms in the 1970's to his groundbreaking results on one-dimensional dynamics. Indeed his interest in one-dimensional dynamics is a clear distinction from early influences. An effervescent work in discrete dynamics on the interval and the circle started in the 1970s. It was soon realized that those systems have surprisingly rich dynamics. But, at the same time, an impressive set of tools were developed to study them. There are two main sets of tools. Real methods such as bounded distortion control via Schwarzian derivative and later cross-ratio estimates allows one to understand some of its features. However, often complex methods, with deep connections with Teichmuller theory, are necessary to obtain some of the most striking results. This is especially true in renormalization theory, a theme Welington was very fond of, and that appears prominently in his collected works. Welington played an important role in the development on both fronts, and this book is a testament of his influence in the field which resonates to this day.