Are there Irregular Families of Characteristic Curves?
For Hamiltonian systems of two degrees of freedom the symmetric periodic orbits of a given type appear in continuous families. Every periodic orbit can be represented by one point in some suitable plane of parameters, and the full family is represented by the so called characteristic curve. Some of these curves have components which are isolated, and they are called irregular characteristic curves. In this work we consider one of the examples of this kind of behaviour and we show that if we embed the given Hamiltonian in a one parameter family the components are no longer isolated. Furthermore we give a full explanation of the structure and evolution of those characteristic curves, by using several invariant manifolds.
KeywordsPeriodic Orbit Hamiltonian System Invariant Manifold Parameter Family Characteristic Curf
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