{"title":"Welington De Melo","description":null,"products":[{"product_id":"one-dimensional-dynamics-book-welington-de-melo-9783642780455","title":"One-Dimensional Dynamics","description":"One-dimensional dynamics has developed in the last decades into a subject in its own right. Yet, many recent results are inaccessible and have never been brought together. For this reason, we have tried to give a unified ac count of the subject and complete proofs of many results. To show what results one might expect, the first chapter deals with the theory of circle diffeomorphisms. The remainder of the book is an attempt to develop the analogous theory in the non-invertible case, despite the intrinsic additional difficulties. In this way, we have tried to show that there is a unified theory in one-dimensional dynamics. By reading one or more of the chapters, the reader can quickly reach the frontier of research. Let us quickly summarize the book. The first chapter deals with circle diffeomorphisms and contains a complete proof of the theorem on the smooth linearizability of circle diffeomorphisms due to M. Herman, J.-C. Yoccoz and others. Chapter II treats the kneading theory of Milnor and Thurstonj also included are an exposition on Hofbauer's tower construction and a result on fuB multimodal families (this last result solves a question posed by J. Milnor).","brand":"WoB","offers":[{"title":"GB \/ NEW \/ INGRAM","offer_id":52353440678161,"sku":"NLS9783642780455","price":0.0,"currency_code":"GBP","in_stock":true},{"title":"US \/ NEW \/ INGRAM","offer_id":52761844547857,"sku":"NIN9783642780455","price":0.0,"currency_code":"GBP","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/9783642780455.jpg?v=1758182926"},{"product_id":"welington-de-melo-selected-works-book-welington-de-melo-9783031158339","title":"Welington de Melo - Selected Works","description":"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.","brand":"WoB","offers":[{"title":"GB \/ NEW \/ GARDNERS","offer_id":52418633498897,"sku":"NGR9783031158339","price":0.0,"currency_code":"GBP","in_stock":false}]},{"product_id":"mathematical-aspects-of-quantum-field-theory-book-welington-de-melo-9780521115773","title":"Mathematical Aspects of Quantum Field Theory","description":"Over the last century quantum field theory has made a significant impact on the formulation and solution of mathematical problems and 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 graduate-level 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.","brand":"WoB","offers":[{"title":"GB \/ NEW \/ INGRAM","offer_id":52538938294545,"sku":"NLS9780521115773","price":0.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/9780521115773.jpg?v=1760683576"},{"product_id":"welington-de-melo-selected-works-book-welington-de-melo-9783031158308","title":"Welington de Melo - Selected Works","description":"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.","brand":"WoB","offers":[{"title":"GB \/ NEW \/ GARDNERS","offer_id":52853880455441,"sku":"NGR9783031158308","price":0.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/9783031158308.jpg?v=1764938374"}],"url":"https:\/\/www.worldofbooks.com\/en-gb\/collections\/author-books-by-welington-de-melo.oembed","provider":"World of Books ","version":"1.0","type":"link"}