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151 pages, year 2000, 1Mb PDF

Abstract:

A recent, useful book on dynamical systems theory. Topics from the contents: "Iterations and fixed points 5 1.1 Square roots 5 1.2 Newton's method 7 1.2.1 The guts of the method 7 1.2.2 A vector version 8 1.2.3 Implementation 9 1.2.4 The existence theorem 10 1.2.5 Basins of attraction. . . . . . . . . . . . . . . . . . . . . . 13 1.3 The implicit function theorem 15 1.4 Attractors and repellers . . . . . . . . . . . . . . . . . . . . . . . 17 1.5 Renormalization group . . . . . . . . . . . . . . . . . . . . . . . . 18 2 Bifurcations 25 2.1 The logistic family. . . . . . . . . . . . . . . . . . . . . . . . . . . 25 2.1.7 Reprise. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34 2.2 Local bifurcations. . . . . . . . . . . . . . . . . . . . . . . . . . . 35 2.2.1 The fold. . . 35 2.2.2 Period doubling. . . 38 2.3 Newton's method and Feigenbaum's constant . 43 2.4 Feigenbaum renormalization. . . . . . . . 45 2.5 Period 3 implies all periods . . . . . . . 48 2.6 Intermittency. . . . . . . .59 3.3 Chaos p. 66 3.4 The saw-tooth transformation and the shift . . 67 "

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Open access http://www.math.harvard.edu/~shlomo/

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