Abstract
The investigation of the onset of chaos for a dynamical system which models the nonlinear dynamics of particles in anharmonic potential is analytically performed. It is shown that, in the solutions of the ordinary differential equation which describes this system, a range of parameter values exists for which the system has in its dynamics the so-called Smale horseshoe, which is the source of the unstable chaotic motion observed. Furthermore, using the averaging theorem, the stability of the subharmonics is studied.
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