Asymptotic Differential Algebra And Model Theory Of Transseries

Author : Matthias Aschenbrenner,Lou van den Dries,Joris van der Hoeven
Publisher : Princeton University Press
Page : 880 pages
File Size : 44,5 Mb
Release : 2017-06-06
Category : Mathematics
ISBN : 9781400885411

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Asymptotic Differential Algebra and Model Theory of Transseries by Matthias Aschenbrenner,Lou van den Dries,Joris van der Hoeven Pdf

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 : Matthias Aschenbrenner,Lou Van den Dries,Joris Hoeven
Publisher : Unknown
Page : 849 pages
File Size : 46,6 Mb
Release : 2017
Category : Asymptotic expansions
ISBN : 0691175438

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Asymptotic Differential Algebra and Model Theory of Transseries by Matthias Aschenbrenner,Lou Van den Dries,Joris Hoeven Pdf

Author : Joris van der Hoeven
Publisher : Springer
Page : 260 pages
File Size : 43,7 Mb
Release : 2006-10-31
Category : Mathematics
ISBN : 9783540355915

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Transseries and Real Differential Algebra by Joris van der Hoeven Pdf

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.

Author : Joris van der Hoeven
Publisher : Unknown
Page : 0 pages
File Size : 40,5 Mb
Release : 2006
Category : Difference equations
ISBN : 835403559X

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Transseries and Real Differential Algebra by Joris van der Hoeven Pdf

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.

Author : Joris Hoeven
Publisher : Unknown
Page : 255 pages
File Size : 50,7 Mb
Release : 2006
Category : Differential algebra
ISBN : 661070029X

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Transseries and Real Differential Algebra by Joris Hoeven Pdf

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.

Author : Joris van der Hoeven,Joris Hoeven
Publisher : Springer Science & Business Media
Page : 265 pages
File Size : 55,9 Mb
Release : 2006-09-15
Category : Mathematics
ISBN : 9783540355908

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Transseries and Real Differential Algebra by Joris van der Hoeven,Joris Hoeven Pdf

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.

Author : Fabrizio Broglia
Publisher : American Mathematical Soc.
Page : 366 pages
File Size : 48,7 Mb
Release : 2017
Category : Forms, Quadratic
ISBN : 9781470429669

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Ordered Algebraic Structures and Related Topics by Fabrizio Broglia Pdf

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.

Author : Joan C. Artés,Jaume Llibre,Dana Schlomiuk,Nicolae Vulpe
Publisher : Springer Nature
Page : 699 pages
File Size : 43,9 Mb
Release : 2021-07-19
Category : Mathematics
ISBN : 9783030505707

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Geometric Configurations of Singularities of Planar Polynomial Differential Systems by Joan C. Artés,Jaume Llibre,Dana Schlomiuk,Nicolae Vulpe Pdf

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.

Author : Henri Cartan,Samuel Eilenberg
Publisher : Princeton University Press
Page : 410 pages
File Size : 49,5 Mb
Release : 1999-12-19
Category : Mathematics
ISBN : 0691049912

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Homological Algebra by Henri Cartan,Samuel Eilenberg Pdf

When this book was written, methods of algebraic topology had caused revolutions in the world of pure algebra. To clarify the advances that had been made, Cartan and Eilenberg tried to unify the fields and to construct the framework of a fully fledged theory. The invasion of algebra had occurred on three fronts through the construction of cohomology theories for groups, Lie algebras, and associative algebras. This book presents a single homology (and also cohomology) theory that embodies all three; a large number of results is thus established in a general framework. Subsequently, each of the three theories is singled out by a suitable specialization, and its specific properties are studied. The starting point is the notion of a module over a ring. The primary operations are the tensor product of two modules and the groups of all homomorphisms of one module into another. From these, "higher order" derived of operations are obtained, which enjoy all the properties usually attributed to homology theories. This leads in a natural way to the study of "functors" and of their "derived functors." This mathematical masterpiece will appeal to all mathematicians working in algebraic topology.

Author : Sirakov Boyan,Souza Paulo Ney De,Viana Marcelo
Publisher : World Scientific
Page : 5396 pages
File Size : 52,9 Mb
Release : 2019-02-27
Category : Mathematics
ISBN : 9789813272897

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Proceedings Of The International Congress Of Mathematicians 2018 (Icm 2018) (In 4 Volumes) by Sirakov Boyan,Souza Paulo Ney De,Viana Marcelo Pdf

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.

Author : John T. Baldwin
Publisher : Cambridge University Press
Page : 365 pages
File Size : 52,8 Mb
Release : 2018-01-25
Category : Mathematics
ISBN : 9781107189218

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Model Theory and the Philosophy of Mathematical Practice by John T. Baldwin Pdf

Recounts the modern transformation of model theory and its effects on the philosophy of mathematics and mathematical practice.

Author : Ilijas Farah
Publisher : Springer Nature
Page : 517 pages
File Size : 43,8 Mb
Release : 2019-12-24
Category : Mathematics
ISBN : 9783030270933

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Combinatorial Set Theory of C*-algebras by Ilijas Farah Pdf

This book explores and highlights the fertile interaction between logic and operator algebras, which in recent years has led to the resolution of several long-standing open problems on C*-algebras. The interplay between logic and operator algebras (C*-algebras, in particular) is relatively young and the author is at the forefront of this interaction. The deep level of scholarship contained in these pages is evident and opens doors to operator algebraists interested in learning about the set-theoretic methods relevant to their field, as well as to set-theorists interested in expanding their view to the non-commutative realm of operator algebras. Enough background is included from both subjects to make the book a convenient, self-contained source for students. A fair number of the exercises form an integral part of the text. They are chosen to widen and deepen the material from the corresponding chapters. Some other exercises serve as a warmup for the latter chapters.

Author : Ovidiu Costin
Publisher : CRC Press
Page : 266 pages
File Size : 51,6 Mb
Release : 2008-12-04
Category : Mathematics
ISBN : 9781420070323

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Asymptotics and Borel Summability by Ovidiu Costin Pdf

Incorporating substantial developments from the last thirty years into one resource, Asymptotics and Borel Summability provides a self-contained introduction to asymptotic analysis with special emphasis on topics not covered in traditional asymptotics books. The author explains basic ideas, concepts, and methods of generalized Borel summability, tr

Author : Moshe Jarden,Tony Shaska
Publisher : American Mathematical Soc.
Page : 200 pages
File Size : 51,8 Mb
Release : 2021-05-03
Category : Education
ISBN : 9781470452070

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Abelian Varieties and Number Theory by Moshe Jarden,Tony Shaska Pdf

This book is a collection of articles on Abelian varieties and number theory dedicated to Gerhard Frey's 75th birthday. It contains original articles by experts in the area of arithmetic and algebraic geometry. The articles cover topics on Abelian varieties and finitely generated Galois groups, ranks of Abelian varieties and Mordell-Lang conjecture, Tate-Shafarevich group and isogeny volcanoes, endomorphisms of superelliptic Jacobians, obstructions to local-global principles over semi-global fields, Drinfeld modular varieties, representations of etale fundamental groups and specialization of algebraic cycles, Deuring's theory of constant reductions, etc. The book will be a valuable resource to graduate students and experts working on Abelian varieties and related areas.

Author : Charles F. Miller
Publisher : Princeton University Press
Page : 124 pages
File Size : 54,8 Mb
Release : 1971-11-21
Category : Mathematics
ISBN : 0691080917

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On Group-theoretic Decision Problems and Their Classification by Charles F. Miller Pdf

Part exposition and part presentation of new results, this monograph deals with that area of mathematics which has both combinatorial group theory and mathematical logic in common. Its main topics are the word problem for groups, the conjugacy problem for groups, and the isomorphism problem for groups. The presentation depends on previous results of J. L. Britton, which, with other factual background, are treated in detail.