Consider the Hénon map deacribed by (1.1.5) and (1.1.6). Assume... | Filo
Consider the Hénon map deacribed by (1.1.5) and (1.1.6). Assume... | Filo
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(Hénon's area-preserving quadratic map) The map xω 1=xu cosα-(yn-xn^2) sinα yn 1=xn sinα (yn-xn^2) cosα illustrates many of the remarkable properties of area-preserving maps (Hénon 1969,1983 ). Here 0 ≤α≤πis a parameter. a) Verify that the map is area-preserving. b) Find the inverse mapping. c) Explore the map on the computer for various α, For instance, try cosα=0.24, and use initial conditions in the square -1 ≤x, y ≤1. You should be able to find a lovely chain of five islands surroundi
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