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Section 2.9 The doubling map and chaos. A glance at the cobweb plots of \(f(x)=x^2-2\) and \(g(x)=4x(1-x)\) shows that they both exhibit very complicated behavior. In fact, they are chaotic in a perfectly quantitative sense. In this section, we'll introduce the doubling map, which is (in a sense) the prototypical chaotic map.
Mark McClure May 2, 2017 When we speak of local behavior‘’s, we mean the behavior of a complex analyticfunctionnearsomepoint. Inthissetofnotes,weexaminethebehavior of a complex analytic function near a fixed point or, by extension, near the pointsinaperiodicorbit.