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1.

図書
図書
1. Dynamical chaos : proceedings of a Royal Society discussion meeting held on 4 and 5 February 1987 (pbk.)
organized and edited by M.V. Berry, I.C. Percival and N.O. Weiss
出版情報: London : The Royal Society, 1987  199 p. ; 26 cm
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2.

図書
図書
2. Analysis and simulation of chaotic systems. 2nd ed
Frank C. Hoppensteadt
出版情報: New York : Springer, c2000  xx, 315 p. ; 25 cm
シリーズ名: Applied mathematical sciences ; v. 94
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目次情報: 続きを見る
Linear Systems
Dynamical Systems
Stability Methods for Nonlinear Systems
Bifurcation and Topological Methods
Regular Perturbation Methods
Iterations and Perturbations
Methods of Averaging
Quasistatic-State Approximations
References
Index
Linear Systems
Dynamical Systems
Stability Methods for Nonlinear Systems
3.

図書
図書
3. Discrete chaos
Saber N. Elaydi
出版情報: Boca Raton, Fla. : Chapman & Hall/CRC, c2000  xiii, 355 p. ; 25 cm
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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：
4.

図書
図書
4. Complex systems
edited by Terry R. J. Bossomaier and David G. Green
出版情報: Cambridge : Cambridge University Press, 2000  v, 413 p ; 24cm
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目次情報: 続きを見る
Introduction / T. R. J. Bossomaier ; D. G. Green1：
Self-organisation in complex systems / 2：
Network evolution and the emergence of structure / D. A. Seeley3：
Artificial life: growing complex systems / Z. Aleksic4：
Deterministic and random fractals / John E. Hutchinson5：
Non-linear dynamics / D. E. Stewart ; R. L. Dewar6：
Non-linear control systems / M. R. James7：
Parallel computers and complex systems / G. C. Fox ; P. D. Coddington8：
Are ecosystems complex systems / R. H. Bradbury ; N. Snoad9：
Complexity and neural networks Terry Bossomaier / 10：
Index
Introduction / T. R. J. Bossomaier ; D. G. Green1：
Self-organisation in complex systems / 2：
Network evolution and the emergence of structure / D. A. Seeley3：
5.

図書
図書
5. Controlling chaos and bifurcations in engineering systems
edited by Guanrong Chen
出版情報: Boca Raton, FL : CRC Press, c2000  xvii, 648 p. ; 24 cm
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6.

図書
図書
6. Chaos near resonance
G. Haller
出版情報: New York ; Tokyo : Springer, c1999  xvi, 427 p. ; 25 cm
シリーズ名: Applied mathematical sciences ; 138
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7.

図書
図書
7. Laws of chaos : invariant measures and dynamical systems in one dimension (: us ; : sz)
Abraham Boyarsky, Pawel Góra
出版情報: Boston, Mass : Birkhauser, c1997  xv, 399 p. ; 24 cm
シリーズ名: Probability and its applications
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8.

図書
図書
8. Mathematics of fractals
Masaya Yamaguti, Masayoshi Hata, Jun Kigami ; translated by Kiki Hudson
出版情報: Providence, R.I. : American Mathematical Society, c1997  xi, 78 p. ; 26 cm
シリーズ名: Translations of mathematical monographs ; v. 167
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9.

図書
図書
9. Thermodynamics of chaos and order
Victor L. Berdichevsky
出版情報: Harlow, Essex, England : Longman, 1997  x, 267 p. ; 24 cm
シリーズ名: Pitman monographs and surveys in pure and applied mathematics ; vol. 90
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10.

図書
図書
10. Discreteness and continuity in problems of chaotic dynamics
Michael Blank
出版情報: Providence, R.I. : American Mathematical Society, c1997  xiii, 161 p. ; 26 cm
シリーズ名: Translations of mathematical monographs ; v. 161
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目次情報: 続きを見る
Introduction
Operator approach in chaotic dynamics / Chapter 1：
Random perturbations of dynamical systems / Chapter 2：
Weakly coupled dynamical systems / Chapter 3：
Phase space discretization in dyanmical systems / Chapter 4：
Ergodic properties of some methods for numerical modeling of chaotic dynamics / Chapter 5：
References / Chapter 6：
Index
Introduction
Operator approach in chaotic dynamics / Chapter 1：
Random perturbations of dynamical systems / Chapter 2：
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