On the Number of Limit Cycles Bifurcated from Some Non-Polynomial Hamiltonian Systems

This paper studies the limit cycles produced by small perturbations of certain planar Hamiltonian systems. The limit cycles under consideration correspond to critical levels of the Hamiltonian, that is they are located in a small vicinity of a separatrix contour or a critical point. Two most interesting facts in the paper are that the Hamiltonian function is not a polynomial and that the system under consideration comes from a model of oscillator with a pair of irrational nonlinearities, which implies the transition from smooth to discontinuous dynamics. This model has been proposed recently by Han et al. in a paper published in 2012.