Geometric tools to determine the hyperbolicity of limit cycles ∗

In this paper we present a new method to study limit cycles ’ hyper-bolicity. The main tool is the function ν = ([V,W] ∧ V)/(V ∧W), where V is the vector field under investigation and W a transversal one. Our approach gives a high degree of freedom for choosing operators to study the stability. It is related to the divergence test, but provides more infor-mation on the system’s dynamics. We extend some previous results on hyperbolicity and apply our results to get limit cycles ’ uniqueness. Liénard systems and conservative+dissipative systems are considered among the applications.