# 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: Part One: One-Dimensional Dynamics    1.1 Examples of dynamical systems    1.2 Preliminaries from calculus    1.3 Elementary definitions    1.4 Hyperbolicity    1.5 An example: the quadratic family    1.6 Symbolic dynamics    1.7 Topological conjugacy    1.8 Chaos    1.9 Structural stability    1.10 Sarkovskii's theorem    1.11 The Schwarzian derivative    1.12 Bifurcation theory    1.13 Another view of period three    1.14 Maps of the circle    1.15 Morse-Smale diffeomorphisms    1.16 Homoclinic points and bifurcations    1.17 The period-doubling route to chaos    1.18 The kneading theory    1.19 Genealogy of periodic points  Part Two: Higher Dimensional Dyiianiirs    2.1 Preliminaries from linear algebra and advanced calculus    2.2 The dynamics of linear maps: two and three dimensions    2.3 The horseshoe map    2.4 Hyperbolic toral automorphisms    2.5 Attractors    2.6 The stable and unstable manifold theorem    2.7 Global results and hyperbolic sets    2.8 The Hopf bifurcation    2.9 The Henon map  Part Three: Complex Analytic Dynamics    3.1 Preliminaries from complex analysis    3.2 Quadratic maps revisited    3.3 Normal families and exceptional points    3.4 Periodic points    3.5 The Julia set    3.6 The geometry of Julia sets    3.7 Neutral periodic points    3.8 The Mandelbrot set    3.9 An example: the exponential function  Color Plates  Index  Формат: djvu Размер: 3179443 байт Язык: ENG Рейтинг: 205 Открыть: Нет поддержки JS :(