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1.

図書
図書
1. 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：
2.

図書
図書
2. 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：
3.

図書
図書
3. Surveying a dynamical system : a study of the Gray-Scott reaction in a two-phase reactor
Khalid Alhumaizi and Rutherford Aris
出版情報: Harlow : Longman, 1995  328 p. ; 25 cm
シリーズ名: Pitman research notes in mathematics series ; 341
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4.

図書
図書
4. Dynamical systems with hyperbolic behaviour (: gw ; : us)
D.V. Anosov (ed.)
出版情報: Berlin ; Tokyo : Springer-Verlag, c1995  235 p. ; 24 cm
シリーズ名: Encyclopaedia of mathematical sciences / editor-in-chief, R.V. Gamkrelidze ; v. 66 . Dynamical systems ; 9
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目次情報:
Elliptic Boundary Problems / M.S. Agranovich
Boundary Value Problems for Elliptic Pseudodifferential Operators / A.V. Brenner ; E.M. Shargorodsky
Elliptic Boundary Value Problems in Domains with Piecewise Smooth Boundary / B.A. Plamenevskij
Elliptic Boundary Problems / M.S. Agranovich
Boundary Value Problems for Elliptic Pseudodifferential Operators / A.V. Brenner ; E.M. Shargorodsky
Elliptic Boundary Value Problems in Domains with Piecewise Smooth Boundary / B.A. Plamenevskij
5.

図書
図書
5. Chaos : an introduction to dynamical systems
Kathleen T. Alligood, Tim D. Sauer, James A. Yorke
出版情報: New York : Springer, c1996  xvii, 603 p., [8] p. of plates ; 24 cm
シリーズ名: Textbooks in mathematical sciences
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6.

図書
図書
6. Chaotic behaviour of deterministic dissipative systems
Miloš Marek, Igor Schreiber
出版情報: Cambridge [Cambridgeshire] ; New York : Cambridge University Press, 1991  x, 367 p. ; 25 cm
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目次情報: 続きを見る
Introduction
Differential equations, maps and asymptotic behaviour / 1：
Transition from order to chaos / 2：
Numerical methods for studies of parametric dependences, bifurcations and chaos / 3：
Chaotic dynamics in experiments / 4：
Forced and coupled chemical oscillators: a case study of chaos / 5：
Chaos in distributed systems / 6：
Appendices
Bibliography
Index
Introduction
Differential equations, maps and asymptotic behaviour / 1：
Transition from order to chaos / 2：
7.

図書
図書
7. An introduction to chaotic dynamical systems. 2nd ed
Robert L. Devaney
出版情報: Redwood City, Calif. ; Tokyo : Addison-Wesley Pub. Co., c1989  xvi, 336 p., [8] p. of col. plates ; 25 cm
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8.

図書
図書
8. Elementary symbolic dynamics and chaos in dissipative systems (:hard ; :pbk.)
Hao Bai-lin
出版情報: Singapore ; Teaneck, N.J. : World Scientific, c1989  xv, 460 p. ; 23 cm
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9.

図書
図書
9. Hyperbolicity and sensitive chaotic dynamics at homoclinic bifurcations : fractal dimensions and infinitely many attractors
Jacob Palis, Floris Takens
出版情報: Cambridge [England] : Cambridge University Press, 1993  x, 234 p. ; 24 cm
シリーズ名: Cambridge studies in advanced mathematics ; 35
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10.

図書
図書
10. Introduction to applied nonlinear dynamical systems and chaos (: us ; : gw)
Stephen Wiggins
出版情報: New York ; Tokyo : Springer-Verlag, c1990  xiv, 672 p. ; 25 cm
シリーズ名: Texts in applied mathematics ; 2
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