Galois theory of difference equations

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Galois theory of difference equations / Marius van der Put, Michael F. Singer

資料種別:

図書

出版情報:

Berlin ; New York : Springer, c1997

形態:

vii, 178 p. ; 24 cm

シリーズ名:

Lecture notes in mathematics ; 1666 <BA00146586>

著者名:

ISBN:

9783540632436 [3540632433]

書誌ID:

BA32562809

子書誌情報

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書誌詳細

注記:

Includes bibliography (p. [175]-178) and index

主題:

Difference equations; Galois theory

言語:

英語

目次情報:

Algebraic Theory

Picard-Vessiot rings / 1：

Existence and uniqueness of Picard-Vessiot rings / 1.1：

The Galois group / 1.2：

Galois correspondence for difference equations / 1.3：

Difference modules and fibre functors / 1.4：

Algorithms for difference equations / 2：

Difference equations of order one / 2.1：

Difference equations in diagonal form / 2.2：

Difference equations of order two / 2.3：

The inverse problem for difference equations / 3：

The ring S of sequences / 4：

An excursion in positive characteristic / 5：

Generalities / 5.1：

Modules over K[T. T superscript -1] / 5.2：

Difference Galois groups / 5.3：

Comparing characteristic 0 and p / 5.4：

Difference modules over P / 6：

Classification of difference modules over P / 6.1：

The universal Picard-Vessiot ring of P / 6.2：

Fields of constants which are not algebraically closed / 6.3：

Automorphisms of the universal Picard-Vessiot ring of P / 6.4：

Difference equations over C((z[superscript -1])) and the formal Galois group / 6.5：

Analytic Theory

Classification and canonical forms / 7：

A classification of singularities / 7.1：

Canonical forms / 7.2：

Semi-regular difference equations / 8：

Introduction / 8.1：

Some easy asymptotics / 8.2：

The connection matrix of a semi-regular equation / 8.3：

The theorem of Malgrange and Sibuya / 8.4：

Regular difference equations / 8.5：

Inverse problems for semi-regular equations / 8.6：

Mild difference equations / 9：

Asymptotics for mild equations / 9.1：

Connection matrices of mild equations / 9.2：

Tame differential modules / 9.3：

Inverse problems for mild equations / 9.4：

Examples of equations and Galois groups / 10：

Calculating connection matrices / 10.1：

Classification of order one equations / 10.2：

More on difference Galois groups / 10.3：

Mild difference and differential equations / 10.4：

Very mild difference modules and multisummability / 10.5：

Very mild differential modules / 10.6：

Wild difference equations / 11：

Multisummability of formal solutions / 11.1：

The Quadrant Theorem / 11.3：

On the Gamma function / 11.4：

An example / 11.5：

Solutions on a right half plane / 11.6：

Solutions on an upper half plane / 11.7：

Analytic equivalence classes of difference equations / 11.8：

q-difference equations / 11.9：

Formal aspects / 12.1：

Analytic properties / 12.2：

Regular singular equations over k[subscript 0] / 12.2.1：

Equations over C(z) / 12.2.2：

Construction of the connection map / 12.3：

Meromorphic vector bundles / 12.3.1：

The connection map of a regular equation / 12.3.2：

The connection map of a regular singular equation / 12.3.3：

Inverse problems / 12.3.4：

Bibliography

Index

Notations

Algebraic Theory

Picard-Vessiot rings / 1：

Existence and uniqueness of Picard-Vessiot rings / 1.1：

The Galois group / 1.2：

Galois correspondence for difference equations / 1.3：

Difference modules and fibre functors / 1.4：

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