THREE DIMENSIONAL SYSTEMS Lecture 6: The Lorenz …

y_ = y Let I denote the interval 1 x 1;y = 0. Is I an attractor? Fig. 6.2.7 So, I is an invariant set (condition 1.). Also, I attracts an open set of initial conditions - it attracts all trajectories in the xy-plane. But I is not an attractor because it is not minimal. The stable xed points ( 1;0) are proper subsets of I that also satisfy condi-

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