"Differential Galois theory"의 두 판 사이의 차이
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| 42번째 줄: | 42번째 줄: | ||
<h5>Picard-Vessiot extension</h5> | <h5>Picard-Vessiot extension</h5> | ||
| + | * this corresponds to | ||
* examples<br> | * examples<br> | ||
** algebraic extension | ** algebraic extension | ||
| 69번째 줄: | 70번째 줄: | ||
* [http://www.google.com/url?sa=t&source=web&ct=res&cd=1&ved=0CA4QFjAA&url=http%3A%2F%2Fwww.iop.org%2FEJ%2Fabstract%2F0036-0279%2F38%2F1%2FR01&ei=lC8vS8nOIYqasgPAxYC7BA&usg=AFQjCNEbFgEgKKkYePd8PTExF9JevV6EQA&sig2=kEI9jPaMRI5NgzmUvWr9tA Integrability and non-integrability in Hamiltonian mechanics] | * [http://www.google.com/url?sa=t&source=web&ct=res&cd=1&ved=0CA4QFjAA&url=http%3A%2F%2Fwww.iop.org%2FEJ%2Fabstract%2F0036-0279%2F38%2F1%2FR01&ei=lC8vS8nOIYqasgPAxYC7BA&usg=AFQjCNEbFgEgKKkYePd8PTExF9JevV6EQA&sig2=kEI9jPaMRI5NgzmUvWr9tA Integrability and non-integrability in Hamiltonian mechanics] | ||
* [http://www.caminos.upm.es/matematicas/morales%20ruiz/libroFSB.pdf ]http://www.caminos.upm.es/matematicas/morales%20ruiz/libroFSB.pdf | * [http://www.caminos.upm.es/matematicas/morales%20ruiz/libroFSB.pdf ]http://www.caminos.upm.es/matematicas/morales%20ruiz/libroFSB.pdf | ||
| − | * [http://andromeda.rutgers.edu/%7Eliguo/DARTIII/Presentations/Khovanskii.pdf http://andromeda.rutgers.edu/~liguo/DARTIII/Presentations/Khovanskii.pdf] | + | * [http://andromeda.rutgers.edu/%7Eliguo/DARTIII/Presentations/Khovanskii.pdf http://andromeda.rutgers.edu/~liguo/DARTIII/Presentations/Khovanskii.pdf] |
| + | * [http://www.math.purdue.edu/%7Eagabriel/topological_galois.pdf http://www.math.purdue.edu/~agabriel/topological_galois.pdf] | ||
2010년 1월 22일 (금) 06:21 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
- this corresponds to
- 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
- Differential Galois Theory and Non-Integrability of Hamiltonian Systems
- Integrability and non-integrability in Hamiltonian mechanics
- [1]http://www.caminos.upm.es/matematicas/morales%20ruiz/libroFSB.pdf
- http://andromeda.rutgers.edu/~liguo/DARTIII/Presentations/Khovanskii.pdf
- http://www.math.purdue.edu/~agabriel/topological_galois.pdf
하위페이지
관련논문
- Liouvillian First Integrals of Differential Equations
- Michael F. Singer, Transactions of the American Mathematical Society, Vol. 333, No. 2 (Oct., 1992), pp. 673-688
표준적인 도서 및 추천도서
- Group Theory and Differential Equations
- Lawrence Markus, 1960
- An introduction to differential algebra
- Irving Kaplansky
- Irving Kaplansky
- algebraic theory of differential equations
- http://gigapedia.info/1/galois_theory
- http://gigapedia.info/1/differential+galois+theory
- http://gigapedia.info/1/Kolchin
- http://gigapedia.info/1/ritt
- http://gigapedia.info/1/Galois'+dream
- http://gigapedia.info/1/differntial+algebra
- http://gigapedia.info/1/
- http://www.amazon.com/s/ref=nb_ss_gw?url=search-alias%3Dstripbooks&field-keywords=