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1.

図書

図書
Valentin Afraimovich and Sze-Bi Hsu
出版情報: Providence : American Mathematical Society : International Press, c2003  ix, 353 p. ; 26 cm
シリーズ名: AMS/IP studies in advanced mathematics ; v. 28
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2.

図書

図書
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:
3.

図書

図書
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:
4.

図書

図書
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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5.

図書

図書
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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6.

図書

図書
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
7.

図書

図書
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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8.

図書

図書
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
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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10.

図書

図書
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:
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