Melo, Welington de
Overview
Works:  27 works in 149 publications in 7 languages and 2,202 library holdings 

Genres:  Conference papers and proceedings 
Roles:  Author, Editor 
Classifications:  QA614, 514.74 
Publication Timeline
.
Most widely held works by
Welington de Melo
Geometric theory of dynamical systems : an introduction by
Jacob Palis Júnior(
Book
)
26 editions published between 1982 and 1998 in 4 languages and held by 455 WorldCat member libraries worldwide
... Cette etude qualitative (des equations difj'erentielles) aura par ellem~me un inter~t du premier ordre ... HENRI POINCARE, 1881. We present in this book a view of the Geometric Theory of Dynamical Systems, which is introductory and yet gives the reader an understanding of some of the basic ideas involved in two important topics: structural stability and genericity. This theory has been considered by many mathematicians starting with Poincare, Liapunov and Birkhoff. In recent years some of its general aims were established and it experienced considerable development. More than two decades passed between two important events: the work of Andronov and Pontryagin (1937) introducing the basic concept of structural stability and the articles of Peixoto (19581962) proving the density of stable vector fields on surfaces. It was then that Smale enriched the theory substantially by defining as a main objective the search for generic and stable properties and by obtaining results and proposing problems of great relevance in this context. In this same period Hartman and Grobman showed that local stability is a generic property. Soon after this Kupka and Smale successfully attacked the problem for periodic orbits. We intend to give the reader the flavour of this theory by means of many examples and by the systematic proof of the HartmanGrobman and the Stable Manifold Theorems (Chapter 2), the KupkaSmale Theorem (Chapter 3) and Peixoto's Theorem (Chapter 4). Several ofthe proofs we give vii Introduction Vlll are simpler than the original ones and are open to important generalizations
26 editions published between 1982 and 1998 in 4 languages and held by 455 WorldCat member libraries worldwide
... Cette etude qualitative (des equations difj'erentielles) aura par ellem~me un inter~t du premier ordre ... HENRI POINCARE, 1881. We present in this book a view of the Geometric Theory of Dynamical Systems, which is introductory and yet gives the reader an understanding of some of the basic ideas involved in two important topics: structural stability and genericity. This theory has been considered by many mathematicians starting with Poincare, Liapunov and Birkhoff. In recent years some of its general aims were established and it experienced considerable development. More than two decades passed between two important events: the work of Andronov and Pontryagin (1937) introducing the basic concept of structural stability and the articles of Peixoto (19581962) proving the density of stable vector fields on surfaces. It was then that Smale enriched the theory substantially by defining as a main objective the search for generic and stable properties and by obtaining results and proposing problems of great relevance in this context. In this same period Hartman and Grobman showed that local stability is a generic property. Soon after this Kupka and Smale successfully attacked the problem for periodic orbits. We intend to give the reader the flavour of this theory by means of many examples and by the systematic proof of the HartmanGrobman and the Stable Manifold Theorems (Chapter 2), the KupkaSmale Theorem (Chapter 3) and Peixoto's Theorem (Chapter 4). Several ofthe proofs we give vii Introduction Vlll are simpler than the original ones and are open to important generalizations
Onedimensional dynamics by
Welington de Melo(
Book
)
19 editions published between 1993 and 2012 in English and German and held by 395 WorldCat member libraries worldwide
This monograph gives an account of the state of the art in onedimensional dynamical systems. It presents the theory in a unified way emphasizing the similarities and differences between invertible and noninvertible dynamics (i.e., between diffeomorphisms and endomorphisms). It starts with the invertible case: the combinatorial topological, ergodic and smooth structures are analysed extensively. Then it proceeds by showing that endomorphisms have a much richer dynamics, but that the theory for these endomorphisms can still be developed along the same lines and with similar tools. Moreover, holomorphic dynamical systems are shown to be based on similar principles. In fact, it is shown that complex analytic tools are very powerful even for the study of real onedimensional systems. Several results in this book are new. Moreover, the exciting new developments on universality and renormalization due to D. Sullivan, are presented here in full detail for the first time
19 editions published between 1993 and 2012 in English and German and held by 395 WorldCat member libraries worldwide
This monograph gives an account of the state of the art in onedimensional dynamical systems. It presents the theory in a unified way emphasizing the similarities and differences between invertible and noninvertible dynamics (i.e., between diffeomorphisms and endomorphisms). It starts with the invertible case: the combinatorial topological, ergodic and smooth structures are analysed extensively. Then it proceeds by showing that endomorphisms have a much richer dynamics, but that the theory for these endomorphisms can still be developed along the same lines and with similar tools. Moreover, holomorphic dynamical systems are shown to be based on similar principles. In fact, it is shown that complex analytic tools are very powerful even for the study of real onedimensional systems. Several results in this book are new. Moreover, the exciting new developments on universality and renormalization due to D. Sullivan, are presented here in full detail for the first time
Mathematical aspects of quantum field theory by
Edson de Faria(
Book
)
19 editions published between 2007 and 2011 in English and held by 222 WorldCat member libraries worldwide
"Over the last century quantum field theory has made a significant impact on the formulation and solution of mathematical problems and has inspired powerful advances in pure mathematics. However, most accounts are written by physicists, and mathematicians struggle to find clear definitions and statements of the concepts involved. This graduatelevel introduction presents the basic ideas and tools from quantum field theory to a mathematical audience. Topics include classical and quantum mechanics, classical field theory, quantization of classical fields, perturbative quantum field theory, renormalization, and the standard model. The material is also accessible to physicists seeking a better understanding of the mathematical background, providing the necessary tools from differential geometry on such topics as connections and gauge fields, vector and spinor bundles, symmetries, and group representations"
19 editions published between 2007 and 2011 in English and held by 222 WorldCat member libraries worldwide
"Over the last century quantum field theory has made a significant impact on the formulation and solution of mathematical problems and has inspired powerful advances in pure mathematics. However, most accounts are written by physicists, and mathematicians struggle to find clear definitions and statements of the concepts involved. This graduatelevel introduction presents the basic ideas and tools from quantum field theory to a mathematical audience. Topics include classical and quantum mechanics, classical field theory, quantization of classical fields, perturbative quantum field theory, renormalization, and the standard model. The material is also accessible to physicists seeking a better understanding of the mathematical background, providing the necessary tools from differential geometry on such topics as connections and gauge fields, vector and spinor bundles, symmetries, and group representations"
Geometric methods in dynamics : volume in honor of Jacob Palis by International Conference on Dynamical Systems(
Book
)
23 editions published between 2002 and 2003 in English and French and held by 213 WorldCat member libraries worldwide
23 editions published between 2002 and 2003 in English and French and held by 213 WorldCat member libraries worldwide
Mathematical tools for onedimensional dynamics by
Edson de Faria(
Book
)
14 editions published in 2008 in English and held by 188 WorldCat member libraries worldwide
This selfcontained book discusses the major mathematical tools necessary for the study of complex dynamics at an advanced level. Complete proofs of some of the major tools are presented and an appendix considers Riemann surfaces and Teichmüller theory
14 editions published in 2008 in English and held by 188 WorldCat member libraries worldwide
This selfcontained book discusses the major mathematical tools necessary for the study of complex dynamics at an advanced level. Complete proofs of some of the major tools are presented and an appendix considers Riemann surfaces and Teichmüller theory
Introducao aos sistemas dinamicos by
Jacob Palis Júnior(
Book
)
11 editions published between 1975 and 1978 in Portuguese and held by 20 WorldCat member libraries worldwide
11 editions published between 1975 and 1978 in Portuguese and held by 20 WorldCat member libraries worldwide
Estabilidade estrutural em variedades de dimensão 2 by
Welington de Melo(
Book
)
5 editions published between 1972 and 1973 in Portuguese and Undetermined and held by 19 WorldCat member libraries worldwide
5 editions published between 1972 and 1973 in Portuguese and Undetermined and held by 19 WorldCat member libraries worldwide
Jacob Palisselected works by
Jacob Palis Júnior(
Book
)
2 editions published in 2014 in English and held by 16 WorldCat member libraries worldwide
2 editions published in 2014 in English and held by 16 WorldCat member libraries worldwide
Lectures on onedimensional dynamics by
Welington de Melo(
Book
)
3 editions published between 1989 and 1990 in English and held by 11 WorldCat member libraries worldwide
3 editions published between 1989 and 1990 in English and held by 11 WorldCat member libraries worldwide
Selected Works by
Jacob Palis Júnior(
Book
)
2 editions published in 2014 in English and held by 6 WorldCat member libraries worldwide
2 editions published in 2014 in English and held by 6 WorldCat member libraries worldwide
JuliaFatouSullivan theory for real onedimensional dynamics by
Marco Martens(
Book
)
2 editions published in 1988 in English and held by 4 WorldCat member libraries worldwide
2 editions published in 1988 in English and held by 4 WorldCat member libraries worldwide
Diffeomorphisms on surfaces with a finite number of moduli by
Welington de Melo(
Book
)
5 editions published in 1984 in English and Portuguese and held by 4 WorldCat member libraries worldwide
5 editions published in 1984 in English and Portuguese and held by 4 WorldCat member libraries worldwide
One dimensional dynamics : the mathematical tools by
Edson de Faria(
Book
)
2 editions published in 2001 in Portuguese and English and held by 4 WorldCat member libraries worldwide
2 editions published in 2001 in Portuguese and English and held by 4 WorldCat member libraries worldwide
A structure theorem in one dimensional dynamics by
Welington de Melo(
Book
)
3 editions published in 1986 in 3 languages and held by 4 WorldCat member libraries worldwide
3 editions published in 1986 in 3 languages and held by 4 WorldCat member libraries worldwide
Geometric Theory of Dynamical Systems An Introduction by
Jacob Palis Júnior(
)
1 edition published in 1982 in English and held by 3 WorldCat member libraries worldwide
1 edition published in 1982 in English and held by 3 WorldCat member libraries worldwide
Dong tai xi tong de ji he li lun dao yin by li si Pa(
Book
)
1 edition published in 1986 in Chinese and held by 2 WorldCat member libraries worldwide
1 edition published in 1986 in Chinese and held by 2 WorldCat member libraries worldwide
A structure theorem in one dimensional dynamics by
Welington de Melo(
)
1 edition published in 1986 in English and held by 1 WorldCat member library worldwide
1 edition published in 1986 in English and held by 1 WorldCat member library worldwide
Estabilidade estructural em variedades de dimensao 2 by
Welington de Melo(
)
1 edition published in 1972 in Portuguese and held by 1 WorldCat member library worldwide
1 edition published in 1972 in Portuguese and held by 1 WorldCat member library worldwide
A finiteness problem for one dimensional maps by
Welington de Melo(
)
1 edition published in 1984 in English and held by 1 WorldCat member library worldwide
1 edition published in 1984 in English and held by 1 WorldCat member library worldwide
Mathematical Tools for OneDimensional Dynamics. Cambridge Studies in Advanced Mathematics, Volume 115(
)
1 edition published in 2008 in English and held by 0 WorldCat member libraries worldwide
Originating with the pioneering works of P. Fatou and G. Julia, the subject of complex dynamics has seen great advances in recent years. Complex dynamical systems often exhibit rich, chaotic behavior, which yields attractive computer generated pictures, for example the Mandelbrot and Julia sets, which have done much to renew interest in the subject. This selfcontained book discusses the major mathematical tools necessary for the study of complex dynamics at an advanced level. Complete proofs of some of the major tools are presented; some, such as the BersRoyden theorem on holomorphic motions, appear for the very first time in book format. An appendix considers Riemann surfaces and Teichmuller theory. Detailing the very latest research, the book will appeal to graduate students and researchers working in dynamical systems and related fields. Carefully chosen exercises aid understanding and provide a glimpse of further developments in real and complex onedimensional dynamics
1 edition published in 2008 in English and held by 0 WorldCat member libraries worldwide
Originating with the pioneering works of P. Fatou and G. Julia, the subject of complex dynamics has seen great advances in recent years. Complex dynamical systems often exhibit rich, chaotic behavior, which yields attractive computer generated pictures, for example the Mandelbrot and Julia sets, which have done much to renew interest in the subject. This selfcontained book discusses the major mathematical tools necessary for the study of complex dynamics at an advanced level. Complete proofs of some of the major tools are presented; some, such as the BersRoyden theorem on holomorphic motions, appear for the very first time in book format. An appendix considers Riemann surfaces and Teichmuller theory. Detailing the very latest research, the book will appeal to graduate students and researchers working in dynamical systems and related fields. Carefully chosen exercises aid understanding and provide a glimpse of further developments in real and complex onedimensional dynamics
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Related Identities
 Faria, Edson de Author
 Palis Júnior, Jacob Honoree Author
 Strien, Sebastian van 1956
 Palis Júnior, Jacob Honoree Author Dedicatee
 Viana, Marcelo Editor
 Yoccoz, JeanChristophe Editor
 Manning, Anthony
 Instituto de Matemática Pura e Aplicada (Brazil)
 Martens, Marco 1962 Author
 Centre national de la recherche scientifique (France)
Useful Links
Associated Subjects
Bifurcation theory Diffeomorphisms Differentiable dynamical systems Differential topology Distribution (Probability theory) Dynamics Field theory (Physics) Global analysis (Mathematics) Holomorphic functions Mathematics Physics Quantum field theory Quantum field theoryMathematics Riemann surfaces Teichmüller spaces
Alternative Names
De Melo, Welington
De Melo, Welington 1946
Di Melu, V.
Di Melu, V. 1946
Melo, W. de 1946
Melo, W. de 19462016
Melo, Welington de
Melu, V. Di.
Welington de Melo brasilianischer Mathematiker
Welington de Melo Brazilian mathematician
Welington de Melo wiskundige uit Brazilië
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