close
1.

図書
図書
1. Differential and difference equations
Louis Brand
出版情報: New York : Wiley, c1966  xvi, 698 p. ; 24 cm
所蔵情報: loading…
2.

図書
図書
2. Discrete mechanics : a unified approach
Hayrettin Kardestuncer
出版情報: Wien ; New York : Springer ([in Komm.]), 1975  59 p. ; 24 cm
シリーズ名: CISM courses and lectures ; no. 221
所蔵情報: loading…
3.

図書
図書
3. Discrete-time systems : an introduction with interdisciplinary applications
James A. Cadzow
出版情報: Englewood Cliffs, N.J. : Prentice-Hall, c1973  xix, 440 p. ; 24 cm
シリーズ名: Prentice-Hall computer applications in electrical engineering series
所蔵情報: loading…
4.

図書
図書
4. Difference methods and their extrapolations (: U.S. ; : Germany)
G.I. Marchuk, V.V. Shaidurov
出版情報: New York ; Tokyo : Springer-Verlag, c1983  x, 334 p. ; 25 cm
シリーズ名: Applications of mathematics ; 19
所蔵情報: loading…
5.

図書
図書
5. Discrete chaos
Saber N. Elaydi
出版情報: Boca Raton, Fla. : Chapman & Hall/CRC, c2000  xiii, 355 p. ; 25 cm
所蔵情報: loading…
目次情報: 続きを見る
List of Symbols
Preface
The Stability of One-Dimensional Maps / 1：
Maps vs. Difference Equations / 1.1：
Maps vs. Differential Equations / 1.2：
Linear Maps/Difference Equations / 1.3：
Fixed (Equilibrium) Points / 1.4：
Graphical Iteration and Stability / 1.5：
Criteria for Stability / 1.6：
Hyperbolic Fixed Points / 1.6.1：
Nonhyperbolic Fixed Points / 1.6.2：
Periodic Points and their Stability / 1.7：
The Period-Doubling Route to Chaos / 1.8：
Fixed Points / 1.8.1：
2-Cycles / 1.8.2：
2[superscript 2]-Cycles / 1.8.3：
Beyond [mu][characters not reproducible] / 1.8.4：
Applications / 1.9：
A Genotype Selection Model / 1.9.1：
Sharkovsky's Theorem and Bifurcation / 2：
The Mystery of Period 3 / 2.1：
Converse of Sharkovsky's Theorem / 2.2：
Basin of Attraction / 2.3：
The Schwarzian Derivative / 2.4：
Bifurcation / 2.5：
The Lorenz Map / 2.6：
Appendix
Chaos in One Dimension / 3：
Introduction / 3.1：
Metric Spaces / 3.2：
Transitivity / 3.3：
Sensitive Dependence and Liapunov Exponents / 3.4：
Definition of Chaos / 3.5：
Symbolic Dynamics / 3.6：
Conjugacy / 3.7：
Stability of Two-Dimensional Maps / 4：
Linear Maps vs. Linear Systems / 4.1：
Computing A[superscript n] / 4.2：
Fundamental Set of Solutions / 4.3：
Second-Order Difference Equations / 4.4：
Phase Space Diagrams / 4.5：
Stability Notions / 4.6：
Stability of Linear Systems / 4.7：
Liapunov Functions for Nonlinear Maps / 4.8：
Linear Systems Revisited / 4.9：
Stability via Linearization / 4.10：
The Hartman-Grobman Theorem / 4.10.1：
The Stable Manifold Theorem / 4.10.2：
The Kicked Rotator and the Henon Map / 4.11：
The Henon Map / 4.11.2：
Discrete Epidemic Model for Gonorrhea / 4.11.3：
Perennial Grass / 4.11.4：
Chaos in Two Dimensions / 5：
Hyperbolic Anosov Toral Automorphism / 5.1：
Subshifts of Finite Type / 5.2：
The Horseshoe and Henon Maps / 5.3：
The Henon Map Revisited / 5.3.1：
Center Manifolds / 5.4：
Neimark-Sacker (Hopf) Bifurcation / 5.5：
Fractals / 6：
Examples of Fractals / 6.1：
The Dimension of a Fractal / 6.2：
Iterated Function System / 6.3：
Mathematical Foundation of Fractals / 6.4：
The Collage Theorem and Image Compression / 6.5：
The Julia and Mandelbrot Sets / 7：
Mapping by Functions on the Complex Domain / 7.1：
The Riemann Sphere / 7.2：
The Julia Set / 7.3：
Topological Properties of the Julia Set / 7.4：
Newton's Method in the Complex Plane / 7.5：
The Mandelbrot Set / 7.6：
Bibliography
Answers to Selected Problems
Index
List of Symbols
Preface
The Stability of One-Dimensional Maps / 1：
6.

図書
図書
6. An introduction to difference equations. 2nd ed (: hard)
Saber N. Elaydi
出版情報: New York : Springer, c1999  xviii, 427 p. ; 24 cm
シリーズ名: Undergraduate texts in mathematics
所蔵情報: loading…
7.

図書
図書
7. Galois theory of difference equations
Marius van der Put, Michael F. Singer
出版情報: Berlin ; New York : Springer, c1997  vii, 178 p. ; 24 cm
シリーズ名: Lecture notes in mathematics ; 1666
所蔵情報: loading…
目次情報: 続きを見る
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：
8.

図書
図書
8. Volterra-Stieltjes integral equations and generalized ordinary differential expressions (: Berlin ; : New York)
Angelo B. Mingarelli
出版情報: Berlin ; New York : Springer-Verlag, 1983  xiv, 317 p. ; 25 cm
シリーズ名: Lecture notes in mathematics ; 989
所蔵情報: loading…
9.

図書
図書
9. Dynamic systems on measure chains
by V. Lakshmikantham, S. Sivasundaram and B. Kaymakcalan
出版情報: Dordrecht : Kluwer, c1996  x, 285 p. ; 25 cm
シリーズ名: Mathematics and its applications ; v. 370
所蔵情報: loading…
10.

図書
図書
10. Difference methods for initial-value problems. 2nd ed
Robert D. Richtmyer, K.W. Morton
出版情報: Malabar, Fla. : Krieger Pub. Co., 1994  xiv, 405 p. ; 24 cm
所蔵情報: loading…
文献の複写および貸借の依頼を行う
 文献複写・貸借依頼