Lecture 9, for Tuesday, February 27....

So for tomorrow, I will leave our final example of a 3-dimensional Poincare Map (a First Return Map) and discuss just one more example of relatively simply dynamics, that of the Logistic Map (Section 2.6).  It is a family of maps, parameterized by a single parameter.  It is also a very complicated one.  However, for a certain interval of parameter values, it is quite simple to describe the dynamics.  Although even here, there are clues to future complications. 

We will return to the example I ended with at a later date.

After we spend some time with the Logistic Map, we will step through some of the parts of Chapter 3 that will be important for later.

Chapter 3, in the whole, is a place to dig deeper into some of the more subtle aspects of spaces, metrics and continuous maps that are the objects of dynamical systems.  We will touch on a few topics, like equivalent metrics, continuity using metrics, and some non-Euclidean spaces.  We will leave the rest for moments when context dictates.

For now, read 2.6, 3.1, and 3.2, particularly 3.2.2 in this last section.

See you tomorrow. 

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