Lecture 11 - Tue 2020 10 06 - Virtual
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(1-2) are from Lecture 9
(1) Example of a conservative system: double well and pendulum.

(2) Introduce/define reversible system [invariance t to -t and y to -y].
    Theorem: For reversible systems, linear centers stay centers.

(3) Index theory:
    Definition of index [need isolated critical point].
    Example for Saddle Point [-1].
    Properties of the index.

(4) Cycle graphs.
    Example via homoclynic connections [e.g.: as in (1)]
    More complicated examples [pictorial].
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