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:
An Introduction to chaotic dynamical systems. Second edition — обложка книги.
Part One: One-Dimensional Dynamics [1]
  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
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