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1.

図書
図書
1. Continuous and discrete dynamics near manifolds of equilibria (: gw ; : us)
Bernd Aulbach
出版情報: Berlin ; New York : Springer-Verlag, 1984  ix, 142 p. ; 25 cm
シリーズ名: Lecture notes in mathematics ; 1058
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2.

図書
図書
2. Random perturbations of dynamical systems (: Boston ; : Basel)
Yuri Kifer
出版情報: Boston ; Basel : Birkhäuser, 1988  294 p. ; 24 cm
シリーズ名: Progress in probability and statistics ; v. 16
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3.

図書
図書
3. Smooth dynamical systems
M.C. Irwin
出版情報: London ; New York ; Tokyo : Academic Press, 1980  x, 259 p. ; 24 cm
シリーズ名: Pure and applied mathematics ; 94
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4.

図書
図書
4. Dynamical systems. Rev. ed
by George D. Birkhoff
出版情報: New York ; Providence, R.I. : American Mathematical Society, 1966  xii, 305 p. ; 24 cm
シリーズ名: Colloquium publications / American Mathematical Society ; v. 9
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目次情報: 続きを見る
Physical aspects of dynamical systems Variational principles and applications
Formal aspects of dynamics
Stability of periodic motions
Existence of periodic motions
Application of Poincare's geometric theorem
General theory of dynamical systems
The case of two degrees of freedom
The problem of three bodies
Addendum Footnotes
Bibliography
Index
Physical aspects of dynamical systems Variational principles and applications
Formal aspects of dynamics
Stability of periodic motions
5.

図書
図書
5. Homology and dynamical systems (: pbk)
by John M. Franks
出版情報: Providence, R.I. : Published for the Conference Board of the Mathematical Sciences by the American Mathematical Society, c1982  viii, 120 p. ; 25 cm
シリーズ名: Regional conference series in mathematics ; no. 49
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目次情報: 続きを見る
Hyperbolic chain recurrent sets Morse gradients Symbolic dynamics for basic sets
Smale diffeomorphisms Zeta functions Morse inequalities
Morse-Smale diffeomorphisms Morse-Smale flows Smale flows Flows on $S^3$ Beyond the theme
Subshifts as basic sets / Appendix A：
Constructing fitted diffeomorphisms / Appendix B：
References
Hyperbolic chain recurrent sets Morse gradients Symbolic dynamics for basic sets
Smale diffeomorphisms Zeta functions Morse inequalities
Morse-Smale diffeomorphisms Morse-Smale flows Smale flows Flows on $S^3$ Beyond the theme
6.

図書
図書
6. Recurrences and discrete dynamic systems (: Berlin ; : New York)
Igor Gumowski, Christian Mira
出版情報: Berlin ; New York : Springer-Verlag, 1980  vi, 272 p. ; 25 cm
シリーズ名: Lecture notes in mathematics ; 809
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7.

図書
図書
7. Dynamical systems : a differential geometric approach to symmetry and reduction
Giuseppe Marmo ... [et al.]
出版情報: Chichester, Sussex, England ; New York : Wiley, c1985  xii, 377 p. ; 24 cm
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8.

図書
図書
8. Iterated maps on the interval as dynamical systems (: sz ; : us)
Pierre Collet, Jean-Pierre Eckmann
出版情報: Basel ; Boston : Birkhäuser, c1980  vii, 248 p. ; 24 cm
シリーズ名: Progress in physics ; v. 1
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9.

図書
図書
9. Asymptotic behavior of dissipative systems
Jack K. Hale
出版情報: Providence, R.I. : American Mathematical Society, c1988  ix, 198 p. ; 26 cm
シリーズ名: Mathematical surveys and monographs ; no. 25
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10.

図書
図書
10. 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：
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