Lecture 25 - Thu 2024 12 05   One dimensional maps y = f(x).
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Cover, from [UNM] Unimodal Maps Notes [posted on web page with lecture 24]
[#4] Why/How does period 2 happen?
[#5] point 3 (intermittency).
     point 4 (Universality and the U-sequence).

Then:
Why/How does period 3 happen? Mention "period 3 implies chaos" result/theorem.
Why/how do period doubling sequences happen for unimodal maps?
Why/how does self-similarity arise. Rough idea for Feigenbaum's renormalization
    argument.
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                                           Brief introduction to Floquet Theory.
Examples: bouncing drops; ping-pong; upside down pendulum;
          stability of planetary orbits [this was the original motivation, with
Hill examining the stability of the Moon's orbit in the mid-XIX century].
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                                                                         EXTRAS.
In a prior Lecture I mentioned the Liapunov dimension for strange
attractors, but did not explain it at all. With this lecture I post some notes
from the web on "Strange attractors and Lyapunov dimension" as well as an
attempt at a little intuitive motivation for the Lyapunov dimension. 
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