Asymptotic Differential Algebra And Model Theory Of Transseries
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Asymptotic Differential Algebra And Model Theory Of Transseries
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Author : Matthias Aschenbrenner
language : en
Publisher: Princeton University Press
Release Date : 2017-06-06
Asymptotic Differential Algebra And Model Theory Of Transseries written by Matthias Aschenbrenner and has been published by Princeton University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-06-06 with Mathematics categories.
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.
Asymptotic Differential Algebra And Model Theory Of Transseries
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Author : Matthias Aschenbrenner
language : en
Publisher:
Release Date : 2017
Asymptotic Differential Algebra And Model Theory Of Transseries written by Matthias Aschenbrenner and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017 with Asymptotic expansions categories.
Transseries And Real Differential Algebra
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Author : Joris van der Hoeven
language : en
Publisher: Springer
Release Date : 2006-10-31
Transseries And Real Differential Algebra written by Joris van der Hoeven and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-10-31 with Mathematics categories.
Transseries are formal objects constructed from an infinitely large variable x and the reals using infinite summation, exponentiation and logarithm. They are suitable for modeling "strongly monotonic" or "tame" asymptotic solutions to differential equations and find their origin in at least three different areas of mathematics: analysis, model theory and computer algebra. They play a crucial role in Écalle's proof of Dulac's conjecture, which is closely related to Hilbert's 16th problem. The aim of the present book is to give a detailed and self-contained exposition of the theory of transseries, in the hope of making it more accessible to non-specialists.
Transseries And Real Differential Algebra
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Author : Joris van der Hoeven
language : en
Publisher:
Release Date : 2006
Transseries And Real Differential Algebra written by Joris van der Hoeven and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006 with Difference equations categories.
Transseries are formal objects constructed from an infinitely large variable x and the reals using infinite summation, exponentiation and logarithm. They are suitable for modeling "strongly monotonic" or "tame" asymptotic solutions to differential equations and find their origin in at least three different areas of mathematics: analysis, model theory and computer algebra. They play a crucial role in Écalle's proof of Dulac's conjecture, which is closely related to Hilbert's 16th problem. The aim of the present book is to give a detailed and self-contained exposition of the theory of transseries, in the hope of making it more accessible to non-specialists.
Transseries And Real Differential Algebra
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Author : Joris Hoeven
language : en
Publisher:
Release Date : 2006
Transseries And Real Differential Algebra written by Joris Hoeven and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006 with Differential algebra categories.
Transseries are formal objects constructed from an infinitely large variable x and the reals using infinite summation, exponentiation and logarithm. They are suitable for modeling "strongly monotonic" or "tame" asymptotic solutions to differential equations and find their origin in at least three different areas of mathematics: analysis, model theory and computer algebra. They play a crucial role in A0/00calle's proof of Dulac's conjecture, which is closely related to Hilbert's 16th problem. The aim of the present book is to give a detailed and self-contained exposition of the theory of transseries, in the hope of making it more accessible to non-specialists.
Transseries And Real Differential Algebra
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Author : Joris van der Hoeven
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-09-15
Transseries And Real Differential Algebra written by Joris van der Hoeven and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-09-15 with Mathematics categories.
Transseries are formal objects constructed from an infinitely large variable x and the reals using infinite summation, exponentiation and logarithm. They are suitable for modeling "strongly monotonic" or "tame" asymptotic solutions to differential equations and find their origin in at least three different areas of mathematics: analysis, model theory and computer algebra. They play a crucial role in Écalle's proof of Dulac's conjecture, which is closely related to Hilbert's 16th problem. The aim of the present book is to give a detailed and self-contained exposition of the theory of transseries, in the hope of making it more accessible to non-specialists.
Ordered Algebraic Structures And Related Topics
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Author : Fabrizio Broglia
language : en
Publisher: American Mathematical Soc.
Release Date : 2017
Ordered Algebraic Structures And Related Topics written by Fabrizio Broglia and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017 with Forms, Quadratic categories.
This volume contains the proceedings of the international conference ""Ordered Algebraic Structures and Related Topics'', held from October 12-16, 2015, at CIRM, Luminy, Marseilles, France. Papers contained in this volume cover topics in real analytic geometry, real algebra, and real algebraic geometry including complexity issues, model theory of various algebraic and differential structures, Witt equivalence of fields, and the moment problem.
Geometric Configurations Of Singularities Of Planar Polynomial Differential Systems
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Author : Joan C. Artés
language : en
Publisher: Springer Nature
Release Date : 2021-07-19
Geometric Configurations Of Singularities Of Planar Polynomial Differential Systems written by Joan C. Artés and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-07-19 with Mathematics categories.
This book addresses the global study of finite and infinite singularities of planar polynomial differential systems, with special emphasis on quadratic systems. While results covering the degenerate cases of singularities of quadratic systems have been published elsewhere, the proofs for the remaining harder cases were lengthier. This book covers all cases, with half of the content focusing on the last non-degenerate ones. The book contains the complete bifurcation diagram, in the 12-parameter space, of global geometrical configurations of singularities of quadratic systems. The authors’ results provide - for the first time - global information on all singularities of quadratic systems in invariant form and their bifurcations. In addition, a link to a very helpful software package is included. With the help of this software, the study of the algebraic bifurcations becomes much more efficient and less time-consuming. Given its scope, the book will appeal to specialists on polynomial differential systems, pure and applied mathematicians who need to study bifurcation diagrams of families of such systems, Ph.D. students, and postdoctoral fellows.
Proceedings Of The International Congress Of Mathematicians 2018 Icm 2018 In 4 Volumes
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Author : Sirakov Boyan
language : en
Publisher: World Scientific
Release Date : 2019-02-27
Proceedings Of The International Congress Of Mathematicians 2018 Icm 2018 In 4 Volumes written by Sirakov Boyan and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-02-27 with Mathematics categories.
The Proceedings of the ICM publishes the talks, by invited speakers, at the conference organized by the International Mathematical Union every 4 years. It covers several areas of Mathematics and it includes the Fields Medal and Nevanlinna, Gauss and Leelavati Prizes and the Chern Medal laudatios.
Model Theory And The Philosophy Of Mathematical Practice
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Author : John T. Baldwin
language : en
Publisher: Cambridge University Press
Release Date : 2018-01-25
Model Theory And The Philosophy Of Mathematical Practice written by John T. Baldwin and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-01-25 with Mathematics categories.
Recounts the modern transformation of model theory and its effects on the philosophy of mathematics and mathematical practice.