On Finiteness in Differential Equations and Diophantine Geometry is popular PDF and ePub book, written by Dana Schlomiuk in 2005, it is a fantastic choice for those who relish reading online the Mathematics genre. Let's immerse ourselves in this engaging Mathematics book by exploring the summary and details provided below. Remember, On Finiteness in Differential Equations and Diophantine Geometry can be Read Online from any device for your convenience.
On Finiteness in Differential Equations and Diophantine Geometry Book PDF Summary
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.
Detail Book of On Finiteness in Differential Equations and Diophantine Geometry PDF
- Author : Dana Schlomiuk
- Release : 21 September 2024
- Publisher : American Mathematical Soc.
- ISBN : 9780821828052
- Genre : Mathematics
- Total Page : 194 pages
- Language : English
- PDF File Size : 20,5 Mb
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