Lecture 9 - Tue 2020 09 29 - Virtual
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From Lecture 9
Phase Plane [see lecture 8]. Then

EXAMPLES:
Example: center turns into spiral.
Example: x_t = \pm x^3  and  y_t = - y.     [Degenerate Delta = 0 case].
Example: rabbits and sheep                  [page 27 notes, or book].

Introduce Conservative systems:             [page 28 notes, or book].
  Example for mechanical systems with a potential.
  Definition of conservative.
  Theorem: conservative systems do not have attractors.
  Theorem: conservative systems and centers
           [local max./min of E is such].

Examples: double well and pendulum.

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