Hamiltonian chaos

...When |K| << 1 the Kolmogorov-Arnold-Moser (KAM) theorem implies that most of these invariant circles persist.

Chaotic bands near separatrix

You can see that there are chaotic bands at arbitrary small perturbation K value. These bands are similar. Click "Rand" and "Clear" while you get more accurate (random!) picture.

K = 0.1

K = 0.2

Controls: Click mouse with Alt/Ctrl to zoom In/Out. Hold the Shift key to zoom in the vertical direction only. Press <Enter> to set a new K value.

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updated 19 August 2003