"Differential Galois theory"의 두 판 사이의 차이

수학노트
둘러보기로 가기 검색하러 가기
98번째 줄: 98번째 줄:
 
** Michael F. Singer, Transactions of the American Mathematical Society, Vol. 333, No. 2 (Oct., 1992), pp. 673-688
 
** Michael F. Singer, Transactions of the American Mathematical Society, Vol. 333, No. 2 (Oct., 1992), pp. 673-688
 
* Its, A.R. (2003), [http://www.ams.org/notices/200311/fea-its.pdf "The Riemann–Hilbert Problem and Integrable Systems]", Notices of the AMS 50 (11): 1389–1400
 
* Its, A.R. (2003), [http://www.ams.org/notices/200311/fea-its.pdf "The Riemann–Hilbert Problem and Integrable Systems]", Notices of the AMS 50 (11): 1389–1400
−
 
+
*  The Riemann-Hilbert Problem<br>
−
 
+
** Gabriel Chˆenevert
  
 
 
 
 

2010년 1월 8일 (금) 20:44 판

  • differential galois theory
  • Liouville 

 

 

historical origin
  • integration in finite terms
  • quadrature of second order differential equation (Fuchsian differential equation)

 

 

differential field
  •  

 

elementary extension
  • using exponential and logarithm
  • elementary element

 

 

Liouville extension
  • we can adjoin integrals and exponentials of integrals + algbraic extension
  • an element is said to be representable by a generalized quadrature

 

 

Picard-Vessiot extension
  • examples
    • algebraic extension
    • adjoining an integral
    • adjoining the exponential of an integral

 

theorem

If a Picard-Vessiot extension is a Liouville extension, then the Galois group of this extension is solvable.

 

 

Fuchsian differential equation
  • regular singularity
  • indicial equation
    \(x(x-1)+px+q=0\)
     

 

solution by quadrature

 

 

 

하위페이지

 

http://www.caminos.upm.es/matematicas/morales%20ruiz/libroFSB.pdf

 

 

관련논문

 

표준적인 도서 및 추천도서

 

 

참고할만한 자료
원본 주소 "https://wiki.mathnt.net/index.php?title=Differential_Galois_theory&oldid=34880"