An Introduction to chaotic dynamical systems. Second edition
| Автор(ы): | Devaney R. L.
06.10.2007
|
| Год изд.: | 1989 |
| Описание: | This is first of all a Mathematics text. Throughout, authors emphasize the mathematical aspects of the theory of discrete dynamical systems, not the many and diverse applications of this theory. The text begins at a relatively unsophisticated level and, by the end, has progressed so as to require not much more than the typical mathematics education of an engineer or a physicist. Fully three quarters of the text is accessible to students with only a solid advanced calculus and linear algebra background. Of course, a good dose of mathematical sophistication is useful throughout. |
| Оглавление: |
Обложка книги.
1.1 Examples of dynamical systems [2] 1.2 Preliminaries from calculus [8] 1.3 Elementary definitions [17] 1.4 Hyperbolicity [24] 1.5 An example: the quadratic family [31] 1.6 Symbolic dynamics [39] 1.7 Topological conjugacy [44] 1.8 Chaos [48] 1.9 Structural stability [53] 1.10 Sarkovskii's theorem [60] 1.11 The Schwarzian derivative [69] 1.12 Bifurcation theory [80] 1.13 Another view of period three [93] 1.14 Maps of the circle [102] 1.15 Morse-Smale diffeomorphisms [114] 1.16 Homoclinic points and bifurcations [122] 1.17 The period-doubling route to chaos [130] 1.18 The kneading theory [139] 1.19 Genealogy of periodic points [147] Part Two: Higher Dimensional Dyiianiirs [159] 2.1 Preliminaries from linear algebra and advanced calculus [161] 2.2 The dynamics of linear maps: two and three dimensions [173] 2.3 The horseshoe map [181] 2.4 Hyperbolic toral automorphisms [190] 2.5 Attractors [201] 2.6 The stable and unstable manifold theorem [214] 2.7 Global results and hyperbolic sets [232] 2.8 The Hopf bifurcation [240] 2.9 The Henon map [251] Part Three: Complex Analytic Dynamics [260] 3.1 Preliminaries from complex analysis [261] 3.2 Quadratic maps revisited [268] 3.3 Normal families and exceptional points [272] 3.4 Periodic points [276] 3.5 The Julia set [283] 3.6 The geometry of Julia sets [289] 3.7 Neutral periodic points [300] 3.8 The Mandelbrot set [311] 3.9 An example: the exponential function [319] Color Plates [329] Index [333] |
| Формат: | djvu |
| Размер: | 3179443 байт |
| Язык: | ENG |
| Рейтинг: |
179
|
| Открыть: | Ссылка (RU) |