MTH 840 Chaos and Dynamical Systems
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The MTH 840 Chaos and Dynamical Systems course topics can embrace dynamics of maps and first order and second-order differential equations: stability, bifurcations, limit cycles, dissection of systems with quick and slow time scales. Geometric viewpoint, together with section planes, are going to be stressed. Chaotic behavior is going to be introduced within the context of one-variable maps (the logistic), form sets, etc. Applications are going to be drawn from physics and biology.
Course layout:
1. Analysis of the dynamics
2. Dynamics of one-dimensional maps of each interval and therefore the circle
3. Repetition and minimality
4. Elementary bifurcations
5. Sarkovski's theorem
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