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Introduction To Chaotic Dynamical Systems 3rd edition [Kõva köide]

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  • Formaat: Hardback, 434 pages, kõrgus x laius: 234x156 mm, kaal: 866 g, 8 Line drawings, color; 184 Line drawings, black and white; 8 Illustrations, color; 184 Illustrations, black and white
  • Ilmumisaeg: 29-Nov-2021
  • Kirjastus: Chapman & Hall/CRC
  • ISBN-10: 1032150467
  • ISBN-13: 9781032150468
Teised raamatud teemal:
Introduction To Chaotic Dynamical Systems 3rd editionSuurem pilt
  • Formaat: Hardback, 434 pages, kõrgus x laius: 234x156 mm, kaal: 866 g, 8 Line drawings, color; 184 Line drawings, black and white; 8 Illustrations, color; 184 Illustrations, black and white
  • Ilmumisaeg: 29-Nov-2021
  • Kirjastus: Chapman & Hall/CRC
  • ISBN-10: 1032150467
  • ISBN-13: 9781032150468
Teised raamatud teemal:
Püsilink: https://www.kriso.ee/db/9781032150468.html
Märksõnad:
"There is an explosion of interest in dynamical systems in the mathematical community as well as in many areas of science. The results have been truly exciting: systems which once seemed completely intractable from an analytic point of view can now be understood in a geometric or qualitative sense rather easily. Scientists and engineers realize the power and the beauty of the geometric and qualitative techniques. These techniques apply to a number of important nonlinear problems ranging from physics and chemistry to ecology and economics. Computer graphics have allowed us to view the dynamical behavior geometrically. The appearance of incredibly beautiful and intricate objects such as the Mandelbrot set, the Julia set, and other fractals have really piqued interest in the field. This text is aimed primarily at advanced undergraduate and beginning graduate students. Throughout, the author emphasizes the mathematical aspects of the theory of discrete dynamical systems, not the many and diverse applicationsof this theory. The field of dynamical systems and especially the study of chaotic systems has been hailed as one of the important breakthroughs in science in the past century and its importance continues to expand. There is no question that the field isbecoming more and more important in a variety of scientific disciplines"--

This widely used graduate text introduces modern topics in dynamical systems. The author includes new material on complex dynamics leading to key revisions. Striking color photos illustrating both Julia and Mandelbrot sets are included. This book assumes no prior acquaintance with advanced mathematical topics.
Preface to the Third Edition ix
Author xiii
I One Dimensional Dynamics
1(162)
1 A Visual and Historical Tour
3(16)
1.1 Images from Dynamical Systems
3(3)
1.2 A Brief History of Dynamics
6(13)
2 Examples of Dynamical Systems
19(6)
2.1 Population Models
20(3)
2.2 Newton's Method
23(2)
3 Elementary Definitions
25(8)
3.1 Orbits
25(2)
3.2 Geometric Views of Orbits
27(6)
4 Hyperbolicity
33(8)
4.1 Types of Periodic Points
33(4)
4.2 A Glimpse of Bifurcations
37(4)
5 An Example: The Logistic Family
41(8)
5.1 The Simplest Case
41(3)
5.2 The Cantor Set Case
44(5)
6 Symbolic Dynamics
49(4)
6.1 The Sequence Space
49(1)
6.2 The Shift Map
50(3)
7 Topological Conjugacy
53(8)
7.1 The Itinerary Map
53(2)
7.2 Conjugacy
55(6)
8 Chaos
61(6)
9 Structural Stability
67(8)
10 Sharkovsky's Theorem
75(10)
11 The Schwarzian Derivative
85(12)
12 Bifurcations
97(14)
12.1 Examples of Bifurcations
97(5)
12.2 General Bifurcation Theorems
102(9)
13 Another View of Period Three
111(10)
13.1 Subshifts of Finite Type
111(2)
13.2 The Period 3 Case
113(8)
14 The Period-Doubling Route to Chaos
121(14)
14.1 Renormalization
121(4)
14.2 The Orbit Diagram
125(10)
15 Homoclinic Points and Bifurcations
135(8)
15.1 Homoclinic Points
135(3)
15.2 Homoclinic Bifurcations
138(5)
16 Maps of the Circle
143(12)
16.1 Rotation Numbers
144(5)
16.2 The Standard Family
149(6)
17 Morse-Smale Diffeomorphisms
155(8)
II Complex Dynamics
163(128)
18 Quadratic Maps Revisited
165(8)
18.1 The Case c = 0
165(2)
18.2 The Case |c| > 2
167(2)
18.3 The Case c = -2
169(4)
19 Normal Families and Exceptional Points
173(4)
20 Periodic Points
177(8)
20.1 Linearization
177(4)
20.2 Critical Values in the Basins of Attraction
181(4)
21 Properties of the Julia Set
185(6)
22 The Geometry of the Julia Sets
191(20)
22.1 Quadratic Julia Sets
191(8)
22.2 A Julia Set for a Rational Map
199(3)
22.3 Fractals
202(9)
23 Neutral Periodic Points
211(12)
23.1 Rationally Indifferent Periodic Points
211(5)
23.2 Irrationally Indifferent Periodic Points
216(7)
24 The Mandelbrot Set
223(30)
24.1 Connectivity of the Julia Set
223(3)
24.2 The Mandelbrot Set
226(5)
24.3 Complex Bifurcations
231(5)
24.4 Geometry of the Principal Bulbs
236(5)
24.5 External Rays in the Dynamical Plane
241(4)
24.6 External Rays in the Parameter Plane
245(8)
25 Rational Maps
253(22)
25.1 Singular Perturbations
253(1)
25.2 Basic Properties
254(2)
25.3 The Escape Trichotomy
256(6)
25.4 The Special Case n = 2
262(5)
25.5 Sierpinski Holes
267(8)
26 The Exponential Family
275(16)
26.1 The Cantor Bouquet Case
276(4)
26.2 The Julia Set of ez
280(3)
26.3 Indecomposable Continua
283(8)
III Higher Dimensional Dynamics
291(94)
27 Dynamics of Linear Maps
293(10)
27.1 Behavior of Linear Maps
293(4)
27.2 Stable and Unstable Subspaces
297(6)
28 The Smale Horseshoe Map
303(10)
28.1 Symbolic Dynamics
306(7)
29 Hyperbolic Toral Automorphisms
313(12)
29.1 Hyperbolic Toral Automorphisms
314(4)
29.2 Markov Partitions
318(7)
30 Attractors
325(14)
30.1 The Solenoid
325(7)
30.2 The Plykin Attractor
332(7)
31 The Stable and Unstable Manifold Theorem
339(18)
32 Global Results and Hyperbolic Maps
357(8)
33 The Hopf Bifurcation
365(12)
33.1 Planar Bifurcations
365(3)
33.2 Normal Forms
368(5)
33.3 The Hopf Bifurcation Theorem
373(4)
34 The Henon Map
377(8)
A Mathematical Preliminaries
385(28)
A.1 Preliminaries from Calculus
385(7)
A.2 Preliminaries from Geometry and Topology
392(2)
A.3 Preliminaries from Complex Analysis
394(6)
A.4 Preliminaries from Linear Algebra
400(13)
Bibliography 413(4)
Index 417
Robert L. Devaney is currently Professor of Mathematics at Boston University. He received his PhD from the University of California at Berkeley in under the direction of Stephen Smale. He taught at Northwestern University and Tufts University before coming to Boston University in 1980. His main area of research is dynamical systems, primarily complex analytic dynamics, but also including more general ideas about chaotic dynamical systems. Lately, he has become intrigued with the incredibly rich topological aspects of dynamics, including such things as indecomposable continua, Sierpinski curves, and Cantor bouquets. He is also the author of A First Course in Chaotic Dynamical Systems, Second Edition, published by CRC Press.