Steps from EoMs to Arnold's (circle) map

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I am a physicist and a bit lost in synchronization theory (or, better, in mathematical formalism connected to its description). Is there a set of steps to be followed whenever I need to go from equations of motion to circle map?

Since the full generality might be quite challenging, let's consider two coupled nonlinear oscillators (i.e. two coupled 2nd order ODEs or, naturally, four 1st order ODEs).