On homoclinic bifurcations with symmetry

Alice Claire Jukes
This thesis deals with the description of solutions of symmetric dynamical systems that lie in the neighbourhood of a homoclinic or heteroclinic cycle. Homoclinic and heteroclinic cycles are the main mechanism by which complicated behaviour is known to arise in dynamical systems. A starting point for studying the consequences of the existence of homoclinic and heteroclinic cycles is to focus on non-wandering dynamics, that is, solutions that remain in the neighbourhood of such cycles, both...
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