x

One can derive these equations as the Poincare map for the

Rotator dynamics is reversible
x
_{n} = x_{n+1} - p_{n+1} ,
p _{n} = p_{n+1} - K sin x_{n}
(mod 2p ) .The map has reflection symmetries (x, p) -> (-x, -p)
and (p + x, p) ->
(p - x, -p) , i.e. reflections with respect
to the point (0, 0) and the center of the picture
(p, 0) .
Due to |

It is the nonlinear pendulum equations with the Hamiltonian

The separatrix

E.g. the half-width is

[1] *J.D.Meiss*
"Symplectic Maps, Variational Principles, and Transport" Rev.Mod.Phys. **64**, 795-848, (1992)

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