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Welington de Melo - Selected Works

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  • © 2023
  • Latest edition

Overview

Authors:
  1. Welington de Melo

    1. IMPA, Rio de Janeiro, Brazil

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    You can also search for this author in PubMed   Google Scholar

Editors:
  1. Paolo Piccione

    1. Departamento de Matemática, Universidade de São Paulo, São Paulo, Brazil

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    You can also search for this editor in PubMed   Google Scholar

  • Welington de Melo´s Selected Works contains the most important journal publications of this mathematician

  • Welington de Melo was a renowned specialist in dynamical systems and mathematical physics

  • The volume is part of a collaboration project of the Brazilian Mathematical Society and Springer

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Keywords

About this book

Welington de Melo (Guapé, 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.



Authors, Editors and Affiliations

  • Departamento de Matemática, Universidade de São Paulo, São Paulo, Brazil

    Paolo Piccione

  • IMPA, Rio de Janeiro, Brazil

    Welington de Melo

Bibliographic Information

  • Book Title: Welington de Melo - Selected Works

  • Authors: Welington de Melo

  • Editors: Paolo Piccione

  • Publisher: Springer Cham

  • Copyright Information: The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2023

  • Hardcover ISBN: 978-3-031-15830-8Published: 12 January 2023

  • Softcover ISBN: 978-3-031-15833-9Due: 26 January 2024

  • Edition Number: 1

  • Number of Pages: X, 536

  • Number of Illustrations: 13 b/w illustrations

  • Topics: Mathematics, general

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