On Finiteness in Differential Equations and Diophantine Geometry (CRM Monograph Series) by Dana Schlomiuk (PDF)

Description

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.

User’s Reviews

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐よって、物理的にも、カオス（ ＝ 混沌）など存在しません。つまり、神様の秩序ある御支配が、森羅万象を貫（つらぬ）いています。さらに言い換えれば、悪霊どもの出来る事どもには、厳密に、限界 ＝ タガ が嵌（は）められています。但し、神様からの救いの必要十分条件は、イエス・キリストへの信仰です。

⭐

Keywords

Free Download On Finiteness in Differential Equations and Diophantine Geometry (CRM Monograph Series) in PDF format
On Finiteness in Differential Equations and Diophantine Geometry (CRM Monograph Series) PDF Free Download
Download On Finiteness in Differential Equations and Diophantine Geometry (CRM Monograph Series) 2005 PDF Free
On Finiteness in Differential Equations and Diophantine Geometry (CRM Monograph Series) 2005 PDF Free Download
Download On Finiteness in Differential Equations and Diophantine Geometry (CRM Monograph Series) PDF
Free Download Ebook On Finiteness in Differential Equations and Diophantine Geometry (CRM Monograph Series)