"Differential Galois theory"의 두 판 사이의 차이

수학노트
둘러보기로 가기 검색하러 가기
19번째 줄: 19번째 줄:
 
* we can adjoin integrals and exponentials of integrals + algbraic extension
 
* we can adjoin integrals and exponentials of integrals + algbraic extension
 
* an element is said to be representable by a generalized quadrature
 
* an element is said to be representable by a generalized quadrature
 +
 +
 
  
 
 
 
 
34번째 줄: 36번째 줄:
  
 
If a Picard-Vessiot extension is a Liouville extension, then the Galois group of this extension is solvable.
 
If a Picard-Vessiot extension is a Liouville extension, then the Galois group of this extension is solvable.
 +
 +
 
 +
 +
 
 +
 +
<h5>Fuchsian differential equation</h5>
 +
 +
* regular singularity
 +
*  
 +
 +
 
  
 
 
 
 

2009년 12월 22일 (화) 09:39 판

  • adele and idele
  • differential galois theory
  • Liouville 

 

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
  •  

 

 

solution by quadrature

 

 

Differential Galois Theory and Non-Integrability of Hamiltonian Systems

Integrability and non-integrability in Hamiltonian mechanic

 

 

하위페이지

 

 

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

표준적인 도서 및 추천도서
  • Abel_s_theorem_by_Arnold.djvu
  • arnold book on abel theorem problem 348
  • An introduction to differential algebra
    • Irving Kaplansky
  • algebraic theory of differential equations

 

 

참고할만한 자료
원본 주소 "https://wiki.mathnt.net/index.php?title=Differential_Galois_theory&oldid=34867"