Recurrence Plots and and Unstable Periodic Orbits:

Each of the following three figures digs more deeply into one of the Lorenz system trajectories on the previous page: (a) a chaotic trajectory (b) an unstable two-cycle in that attractor and (c) an unstable five-cycle in that attractor.

Each figure first shows the trajectory, in 3D and in x-z projection. Those images are followed by a row of RPs of the corresponding trajectory, constructed using the euclidean norm on the x, y, and z components, separately and in 3D. The bottom row of RPs is identical, except it used the max norm.

Note that while the form of the structures differ across the rows, the compositional relationship of the blocks and the whole remains the same, regardless of what component(s) of the trajectory are included in the distance calculation.

Note, too, that the choice of norm does not affect the

The full trajectory:

The two-cycle:

The five-cycle: