Lorentz attractor

Lorentz attractor
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One dimensional maps can help to understand ordinary differential equations::
If you cut the Lorentz attractor at a suitable place with a plane, the intersection points form a pointset lies approximately on an interval. This means that if we look at a solution curve which starts on a point of that interval, the next time this curve will intersect the plane will again be on that interval. This return map is essentially a map on the interval. Indeed, when changing the parameters of the differential equation one finds bifurcation diagrams for periodic flow lines similar to the bifurcation diagram for the logistic map.



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