The `Levenberg-Marquardt' minimization came up. I found a link to it for those that are interested.
We covered the various bifurcations that can happen in 1-D mappings. This is discussed in the book and notes. In addition there are 1-D maps on the circle. This is discussed later in the book, (page 218) and hopefully we will get a chance to cover it.
I discussed fixed point creation in maps of the interval. Pitchfork, inverse pitch fork and tangent bifurcations are the generic methods that fixed points appear as a function of control parameter. The period doubling transition was discovered by Cvitanovic and Feigenbaum.
Various examples of mappings were shown to see the range of behavior that can occur. This included the ``standard map'', ``maps of the torus'', "Henon map." Standard map and Henon map can be found in the textbook and particularly the standard map has been intensively studied with key advances made by Greene and Mackay. References on the torus map can be found on the net. Computer code is linked
on the home page.
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