This book presents two essential and apparently unrelated subjects. The first, microlocal analysis and the theory of pseudo-differential operators, is a basic tool in the study of partial differential equations and in analysis on manifolds. The second, the Nash-Moser theorem, continues to be fundamentally important in geometry, dynamical systems and nonlinear PDE. Each of the subjects, which are of interest in their own right as well as for applications, can be learned separately. But the book shows the deep connections between the two themes, particularly in the middle part, which is devoted to Littlewood-Paley theory, dyadic analysis, and the paradifferential calculus and its application to interpolation inequalities. An important feature is the elementary and self-contained character of the text, to which many exercises and an introductory Chapter $0$ with basic material have been added. This makes the book readable by graduate students or researchers from one subject who are interested in becoming familiar with the other. It can also be used as a textbook for a graduate course on nonlinear PDE or geometry.
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"In fuga dagli Sceriffi" era gi l negli anni Ottanta: bastava viverli senza la prospettiva di un posto comodo, ben remunerato, o da tifoso strillone e fanatico.Il libro ricostruisce la storia di quel ciclismo dal concetto stesso dello sport della bici: fa dunque a meno di un immaginario di cartone, falsato nelle prospettive e nella sostanza, che diventato uno stereotipo (comodo).Utilizzando un universo, come il ciclismo, ricco di storie come nessun altro in Europa: il nostro baseball?In fondo, qualsiasi difetto gli si possa trovare, In fuga dagli sceriffi soddisfa una missione possibile quanto ambiziosa: proporre un'opera - sportiva - mai scritta prima.
INTRODUCTION TO ARNOLD’S PROOF OF THE KOLMOGOROV–ARNOLD–MOSER THEOREMThis book provides an accessible step-by-step account of Arnold’s classical proof of the Kolmogorov–Arnold–Moser (KAM) Theorem. It begins with a general background of the theorem, proves the famous Liouville–Arnold theorem for integrable systems and introduces Kneser’s tori in four-dimensional phase space. It then introduces and discusses the ideas and techniques used in Arnold’s proof, before the second half of the book walks the reader through a detailed account of Arnold’s proof with all the required steps. It will be a useful guide for advanced students of mathematical physics, in addition to researchers and professionals.Features• Applies concepts and theorems from real and complex analysis (e.g., Fourier series and implicit function theorem) and topology in the framework of this key theorem from mathematical physics.• Covers all aspects of Arnold’s proof, including those often left out in more general or simplifi ed presentations.• Discusses in detail the ideas used in the proof of the KAM theorem and puts them in historical context (e.g., mapping degree from algebraic topology).
INTRODUCTION TO ARNOLD’S PROOF OF THE KOLMOGOROV–ARNOLD–MOSER THEOREMThis book provides an accessible step-by-step account of Arnold’s classical proof of the Kolmogorov–Arnold–Moser (KAM) Theorem. It begins with a general background of the theorem, proves the famous Liouville–Arnold theorem for integrable systems and introduces Kneser’s tori in four-dimensional phase space. It then introduces and discusses the ideas and techniques used in Arnold’s proof, before the second half of the book walks the reader through a detailed account of Arnold’s proof with all the required steps. It will be a useful guide for advanced students of mathematical physics, in addition to researchers and professionals.Features• Applies concepts and theorems from real and complex analysis (e.g., Fourier series and implicit function theorem) and topology in the framework of this key theorem from mathematical physics.• Covers all aspects of Arnold’s proof, including those often left out in more general or simplifi ed presentations.• Discusses in detail the ideas used in the proof of the KAM theorem and puts them in historical context (e.g., mapping degree from algebraic topology).