Welington de Melo (Guape, 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.
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