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Limit cycles of the Liénard systems
- Introduction
We have introduced a formal algorithm and conjectured that it may yield the number, multiplicity and location of the limit cycles of the Lienard equation. The difficult problem of finding these limit cycles is reduced to a simpler one of finding the roots of some polynomials. If proved, this conjecture would be a first and important step in the solving of Hilbert 16th problem.
Lienard systems model systems that exhibit relaxation oscillations. A simple example is a bucket attached on the top of a flexible culumn.
The dynamics of the system has two times scales. A slow time, during which the bucket is being filled and a fast time when the water is dumped out rapidely.
- The algorithm