Chaos in Toroidal Systems

The oldest example of complicated behavior found in an unconstrained (non-conservative) dynamical system is, as mentioned in the Introduction, that found in the periodically forced van der Pol oscillator [1]. Cartwright and Littlewood’s results were based on painstaking analytical arguments (see the elaboration in [2]). Is it, at the same time, also possible to understand their observations in terms of the simple reinjection principle? The answer is yes. One can even say that these authors were the first to make use of the reinjection principle in order to find nontrivial behavior in a simple dynamical system.