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thank you everyone for coming to this make obsession of this class this will be the first of approximately five that we undertake I might throw in a sixth to better cover certain material before the next month is out and I appreciate the flexibility in your schedule to accommodate these so with in todays lecture Id like to expand on some of the material whose coverage we initiated last time we began last lecture talking about the fact that we can assess the dimensionality of state space given a set of variables they jointly collectively summarize the state to begin them all so if we have that soon we apply say for a model of predator prey on we could characterize the state space plot on much like this and I noted that as a kind of motivating factor that in nonlinear models we often have a model subject to such coupling that the actual state space occupied by the ball is a small fraction a small manifold the thin manifold within this broader overall state space that the model is not e