| xn+1 | = | xn + b - (a/2 )sin(2xn) |
The 1D Circle map is
| xn+1 | = | xn + b - (a/2)sin(2xn) |
For a<1 the map is smooth, monotonic and invertible (the apparent discontinuity towards the middle of the domain is of course simply due to the wrapping of the variable into the unit interval), and the motion is periodic, either unlocked or locked:
| Parameters | Orbit | Spectrum | Motion |
| a=0.5, b=0.6144 | Unlocked | ||
| a=0.5, b=0.66 | Locked |
For a=1 an inflection point develops at x=1
and for a>1 the map is nonmonotonic:
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