1D Circle Map - Demo 1

Basic properties

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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Last modified Wednesday, December 15, 1999
Michael Cross