Azzari, Paride (2016) Homoclinic chaos and the PoincarÃ©-Melnikov method. [Laurea triennale]
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In this thesis is to describe the use of the PoincarÃ©-Melnikov method in the detection of homoclinic phenomena, and hence chaotic dynamics. After a short review of the theory of dynamical system, it is introduced the PoincarÃ©-Melnikov method and its extension to the case of heteroclinic orbits. An application of this method is given in the last chapter, where it is shown a case of success and a case of failure in the detection of chaos. Results are confirmed through numerical evidence.
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