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Chaos and Dynamical Systems [Pehme köide]

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  • Formaat: Paperback / softback, 264 pages, kõrgus x laius: 216x140 mm, 84 b/w illus.
  • Sari: Primers in Complex Systems
  • Ilmumisaeg: 06-Aug-2019
  • Kirjastus: Princeton University Press
  • ISBN-10: 0691161526
  • ISBN-13: 9780691161525
Teised raamatud teemal:
Chaos and Dynamical SystemsSuurem pilt
  • Formaat: Paperback / softback, 264 pages, kõrgus x laius: 216x140 mm, 84 b/w illus.
  • Sari: Primers in Complex Systems
  • Ilmumisaeg: 06-Aug-2019
  • Kirjastus: Princeton University Press
  • ISBN-10: 0691161526
  • ISBN-13: 9780691161525
Teised raamatud teemal:
Püsilink: https://www.kriso.ee/db/9780691161525.html
Märksõnad:

Chaos and Dynamical Systems presents an accessible, clear introduction to dynamical systems and chaos theory, important and exciting areas that have shaped many scientific fields. While the rules governing dynamical systems are well-specified and simple, the behavior of many dynamical systems is remarkably complex. Of particular note, simple deterministic dynamical systems produce output that appears random and for which long-term prediction is impossible. Using little math beyond basic algebra, David Feldman gives readers a grounded, concrete, and concise overview.

In initial chapters, Feldman introduces iterated functions and differential equations. He then surveys the key concepts and results to emerge from dynamical systems: chaos and the butterfly effect, deterministic randomness, bifurcations, universality, phase space, and strange attractors. Throughout, Feldman examines possible scientific implications of these phenomena for the study of complex systems, highlighting the relationships between simplicity and complexity, order and disorder.

Filling the gap between popular accounts of dynamical systems and chaos and textbooks aimed at physicists and mathematicians, Chaos and Dynamical Systems will be highly useful not only to students at the undergraduate and advanced levels, but also to researchers in the natural, social, and biological sciences.

Arvustused

"Feldman succeeds in introducing the reader to the world of dynamic systems and the, almost mythical, chaos that they can produce."---Adhemar Bultheel, European Mathematical Society "[ A] gentle and loving introduction to dynamical systems. . . . Chaos and Dynamical Systems is a book for everyone from the layman to the expert."---David S. Mazel, MAA Reviews

Preface ix
1 Introducing Iterated Functions
1(16)
1.1 Iterated Functions
1(4)
1.2 Thinking Globally
5(2)
1.3 Stability: Attractors and Repellors
7(2)
1.4 Another Example
9(1)
1.5 One More Example
10(4)
1.6 Determinism
14(1)
1.7 Summary
15(2)
2 Introducing Differential liquations
17(28)
2.1 Newton's Law of Cooling
17(4)
2.2 Exact Solutions
21(1)
2.3 Calculus Puzzles
22(2)
2.4 Qualitative Solutions
24(3)
2.5 Numerical Solutions
27(5)
2.6 Putting It All Together
32(3)
2.7 More about Numerical Solutions
35(1)
2.5 Notes on Terminology and Notation
36(3)
2.9 Existence and Uniqueness of Solutions
39(1)
2.10 Determinism and Differential Equations
40(2)
2.11 Iterated Functions vs. Differential Equations
42(2)
2.12 Further Reading
44(1)
3 Interlude: Mathematical Models and the Newtonian Worldview
45(17)
3.1 Why Isn't This the End of the Book?
45(1)
3.2 Newton's Mechanistic World
46(1)
3.3 Laplacian Determinism and the Aspirations of Science
47(3)
3.4 Styles of Mathematical Models
50(4)
3.5 Levels of Models
54(5)
3.6 Pluralistic View of Mathematical Models
59(2)
3.7 Further Reading
61(1)
4 Chaos I: The Butterfly Effect
62(28)
4.1 The Logistic Equation
62(5)
4.2 Periodic Behavior
67(3)
4.3 Aperiodic Behavior
70(4)
4.4 The Butterfly Effect
74(6)
4.5 The Butterfly Effect Defined
80(3)
4.6 Chaos Defined
83(2)
4.7 Lyapunov Exponents
85(5)
5 Chaos II: Deterministic Randomness
90(16)
5.1 Symbolic Dynamics
91(2)
5.2 As Random as a Coin Toss
93(2)
5.3 Deterministic Sources of Randomness
95(4)
5.4 Implications of the Butterfly Effect
99(5)
5.5 Further Reading
104(2)
6 Bifurcations: Sudden Transitions
106(23)
6.1 Logistic Differential Equation
106(3)
6.2 Logistic Equation with Harvest
109(4)
6.3 Bifurcations and Bifurcation Diagrams
113(6)
6.4 General Remarks on Bifurcations
119(1)
6.5 Catastrophes and Tipping Points
120(3)
6.6 Hysteresis
123(5)
6.7 Further Reading
128(1)
7 Universality in Chaos
129(41)
7.1 Logistic Equation Bifurcation Diagram
129(8)
7.2 Exploring the Bifurcation Diagram
137(4)
7.3 Some Words about Emergence
141(2)
7.4 The Period-Doubling Route to Chaos
143(2)
7.5 Universality in Maps
145(4)
7.6 Universality in Physics
149(2)
7.7 Renormalization
151(8)
7.8 Phase Transitions, Critical Phenomena, and Power Laws
159(6)
7.9 Conclusion: Lessons and Limits to Universality
165(4)
7.10 Further Reading
169(1)
8 Higher-Dimensional Systems and Phase Space
170(19)
8.1 A Quick Review of One-Dimensional Differential Equations
170(2)
8.2 Lotka-Volterra Differential Equations
172(4)
8.3 The Phase Plane
176(5)
8.4 Phase Planes in General
181(2)
8.5 The Rossler Equations and Phase Space
183(5)
8.6 Further Reading
188(1)
9 Strange Attractors
189(34)
9.1 Chaos in Three Dimensions
190(5)
9.2 The Rossler Attractor
195(6)
9.3 Strange Attractors
201(2)
9.4 Back to ID: The Lorenz Map
203(4)
9.5 Stretching and Folding
207(3)
9.6 Poincare Maps
210(2)
9.7 Delay Coordinates and Phase Space Reconstruction
212(7)
9.8 Determinism vs. Noise
219(2)
9.9 Further Reading
221(2)
10 Conclusion
223(8)
10.1 Summary
223(2)
10.2 Complex Systems
225(2)
10.3 Emergence(?)
227(2)
10.4 But Not Everything Is Simple
229(1)
10.5 Further Reading
230(1)
10.6 Farewell
230(1)
Bibliography 231(12)
Index 243
David P. Feldman is professor of physics and mathematics at the College of the Atlantic. He is the author of Chaos and Fractals: An Elementary Introduction.