On Finiteness in Differential Equations and Diophantine Geometry ( CRM Monograph Series )

Publication series :CRM Monograph Series

Author: Dana Schlomiuk;Andreĭ A. Bolibrukh;Sergei Yakovenko  

Publisher: American Mathematical Society‎

Publication year: 2017

E-ISBN: 9781470438685

P-ISBN(Paperback): 9780821828052

Subject: O175.28 Mixed Equations

Keyword: 暂无分类

Language: ENG

Access to resources Favorite

Disclaimer: Any content in publications that violate the sovereignty, the constitution or regulations of the PRC is not accepted or approved by CNPIEC.

On Finiteness in Differential Equations and Diophantine Geometry

Description

This book focuses on finiteness conjectures and results in ordinary differential equations 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 ordinary differential equations. 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 which 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. A chapter is devoted to finiteness results in Diophantine geometry obtained by using methods of differential algebra, a connecting element between these parallel developments in the book.

Chapter

Title page

Dedication

Contents

Foreword

Finiteness problems in differential equations and Diophantine geometry

Linear differential equations, Fuchsian inequalities and multiplicities of zeros

Quantitative theory of ordinary differential equations and the tangential Hilbert 16th problem

Around the Hilbert-Arnol’d problem

Finiteness results in differential algebraic geometry and Diophantine geometry

Appendix A. o-minimal structures, real analytic geometry, and transseries

Appendix B. List of lectures

Appendix C. Photographs of some workshop participants

Appendix D. List of participants

Back Cover

The users who browse this book also browse