Lecture Notes On O Minimal Structures And Real Analytic Geometry PDF Download
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Author | : Chris Miller |
Publisher | : Springer Science & Business Media |
Total Pages | : 247 |
Release | : 2012-09-14 |
Genre | : Mathematics |
ISBN | : 1461440416 |
Download Lecture Notes on O-Minimal Structures and Real Analytic Geometry Book in PDF, ePub and Kindle
This volume was produced in conjunction with the Thematic Program in o-Minimal Structures and Real Analytic Geometry, held from January to June of 2009 at the Fields Institute. Five of the six contributions consist of notes from graduate courses associated with the program: Felipe Cano on a new proof of resolution of singularities for planar analytic vector fields; Chris Miller on o-minimality and Hardy fields; Jean-Philippe Rolin on the construction of o-minimal structures from quasianalytic classes; Fernando Sanz on non-oscillatory trajectories of vector fields; and Patrick Speissegger on pfaffian sets. The sixth contribution, by Antongiulio Fornasiero and Tamara Servi, is an adaptation to the nonstandard setting of A.J. Wilkie's construction of o-minimal structures from infinitely differentiable functions. Most of this material is either unavailable elsewhere or spread across many different sources such as research papers, conference proceedings and PhD theses. This book will be a useful tool for graduate students or researchers from related fields who want to learn about expansions of o-minimal structures by solutions, or images thereof, of definable systems of differential equations.
Author | : Springer |
Publisher | : |
Total Pages | : 252 |
Release | : 2012-09-01 |
Genre | : |
ISBN | : 9781461440437 |
Download Lecture Notes on O-Minimal Structures and Real Analytic Geometry Book in PDF, ePub and Kindle
Author | : Mário J. Edmundo |
Publisher | : Cuvillier Verlag |
Total Pages | : 223 |
Release | : 2005 |
Genre | : |
ISBN | : 386537557X |
Download O-minimal Structures Book in PDF, ePub and Kindle
Author | : Lou Van den Dries |
Publisher | : Cambridge University Press |
Total Pages | : 196 |
Release | : 1998-05-07 |
Genre | : Mathematics |
ISBN | : 0521598389 |
Download Tame Topology and O-minimal Structures Book in PDF, ePub and Kindle
These notes give a self-contained treatment of the theory of o-minimal structures from a geometric and topological viewpoint, assuming only rudimentary algebra and analysis. This book should be of interest to model theorists, analytic geometers and topologists.
Author | : Felipe Cano |
Publisher | : Springer Nature |
Total Pages | : 531 |
Release | : |
Genre | : |
ISBN | : 3031524810 |
Download Handbook of Geometry and Topology of Singularities V: Foliations Book in PDF, ePub and Kindle
Author | : Ovidiu Costin |
Publisher | : American Mathematical Soc. |
Total Pages | : 384 |
Release | : 2005 |
Genre | : Mathematics |
ISBN | : 0821834193 |
Download Analyzable Functions and Applications Book in PDF, ePub and Kindle
The theory of analyzable functions is a technique used to study a wide class of asymptotic expansion methods and their applications in analysis, difference and differential equations, partial differential equations and other areas of mathematics. Key ideas in the theory of analyzable functions were laid out by Euler, Cauchy, Stokes, Hardy, E. Borel, and others. Then in the early 1980s, this theory took a great leap forward with the work of J. Ecalle. Similar techniques and conceptsin analysis, logic, applied mathematics and surreal number theory emerged at essentially the same time and developed rapidly through the 1990s. The links among various approaches soon became apparent and this body of ideas is now recognized as a field of its own with numerous applications. Thisvolume stemmed from the International Workshop on Analyzable Functions and Applications held in Edinburgh (Scotland). The contributed articles, written by many leading experts, are suitable for graduate students and researchers interested in asymptotic methods.
Author | : Matthias Aschenbrenner |
Publisher | : Princeton University Press |
Total Pages | : 880 |
Release | : 2017-06-06 |
Genre | : Mathematics |
ISBN | : 1400885418 |
Download Asymptotic Differential Algebra and Model Theory of Transseries Book in PDF, ePub and Kindle
Asymptotic differential algebra seeks to understand the solutions of differential equations and their asymptotics from an algebraic point of view. The differential field of transseries plays a central role in the subject. Besides powers of the variable, these series may contain exponential and logarithmic terms. Over the last thirty years, transseries emerged variously as super-exact asymptotic expansions of return maps of analytic vector fields, in connection with Tarski's problem on the field of reals with exponentiation, and in mathematical physics. Their formal nature also makes them suitable for machine computations in computer algebra systems. This self-contained book validates the intuition that the differential field of transseries is a universal domain for asymptotic differential algebra. It does so by establishing in the realm of transseries a complete elimination theory for systems of algebraic differential equations with asymptotic side conditions. Beginning with background chapters on valuations and differential algebra, the book goes on to develop the basic theory of valued differential fields, including a notion of differential-henselianity. Next, H-fields are singled out among ordered valued differential fields to provide an algebraic setting for the common properties of Hardy fields and the differential field of transseries. The study of their extensions culminates in an analogue of the algebraic closure of a field: the Newton-Liouville closure of an H-field. This paves the way to a quantifier elimination with interesting consequences.
Author | : Dana Schlomiuk |
Publisher | : American Mathematical Soc. |
Total Pages | : 200 |
Release | : |
Genre | : Mathematics |
ISBN | : 9780821869857 |
Download On Finiteness in Differential Equations and Diophantine Geometry Book in PDF, ePub and Kindle
This book focuses on finiteness conjectures and results in ordinary differential equations (ODEs) and Diophantine geometry. During the past twenty-five years, much progress has been achieved on finiteness conjectures, which are the offspring of the second part of Hilbert's 16th problem. Even in its simplest case, this is one of the very few problems on Hilbert's list which remains unsolved. These results are about existence and estimation of finite bounds for the number of limit cycles occurring in certain families of ODEs. The book describes this progress, the methods used (bifurcation theory, asymptotic expansions, methods of differential algebra, or geometry) and the specific results obtained. The finiteness conjectures on limit cycles are part of a larger picture that also includes finiteness problems in other areas of mathematics, in particular those in Diophantine geometry where remarkable results were proved during the same period of time. There is a chapter devoted to finiteness results in D The volume can be used as an independent study text for advanced undergraduates and graduate students studying ODEs or applications of differential algebra to differential equations and Diophantine geometry. It is also is a good entry point for researchers interested these areas, in particular, in limit cycles of ODEs, and in finiteness problems. Contributors to the volume include Andrey Bolibrukh and Alexandru Buium. Available from the AMS by A. Buium is Arithmetic Differential Equations, as Volume 118 in the Mathematical Surveys and Monographs series.
Author | : Santiago Ibáñez |
Publisher | : Springer Science & Business Media |
Total Pages | : 426 |
Release | : 2013-09-20 |
Genre | : Mathematics |
ISBN | : 3642388302 |
Download Progress and Challenges in Dynamical Systems Book in PDF, ePub and Kindle
This book contains papers based on talks given at the International Conference Dynamical Systems: 100 years after Poincaré held at the University of Oviedo, Gijón in Spain, September 2012. It provides an overview of the state of the art in the study of dynamical systems. This book covers a broad range of topics, focusing on discrete and continuous dynamical systems, bifurcation theory, celestial mechanics, delay difference and differential equations, Hamiltonian systems and also the classic challenges in planar vector fields. It also details recent advances and new trends in the field, including applications to a wide range of disciplines such as biology, chemistry, physics and economics. The memory of Henri Poincaré, who laid the foundations of the subject, inspired this exploration of dynamical systems. In honor of this remarkable mathematician, theoretical physicist, engineer and philosopher, the authors have made a special effort to place the reader at the frontiers of current knowledge in the discipline.
Author | : Siegfried Bosch |
Publisher | : Springer |
Total Pages | : 255 |
Release | : 2014-08-22 |
Genre | : Mathematics |
ISBN | : 3319044176 |
Download Lectures on Formal and Rigid Geometry Book in PDF, ePub and Kindle
The aim of this work is to offer a concise and self-contained 'lecture-style' introduction to the theory of classical rigid geometry established by John Tate, together with the formal algebraic geometry approach launched by Michel Raynaud. These Lectures are now viewed commonly as an ideal means of learning advanced rigid geometry, regardless of the reader's level of background. Despite its parsimonious style, the presentation illustrates a number of key facts even more extensively than any other previous work. This Lecture Notes Volume is a revised and slightly expanded version of a preprint that appeared in 2005 at the University of Münster's Collaborative Research Center "Geometrical Structures in Mathematics".