Abstract
The author considers a reversible system admitting a symmetric periodic orbit such that the Jordan block belonging to the Floquet exponent zero is four-dimensional, nonsemisimple. Using the normal form theory around closed orbits, it is shown that, generically, such a solution is part of a one-parameter family of symmetric periodic orbits. The existence in such a system of two one-parameter families of symmetric solutions homoclinic to some periodic orbits is also proven. Finally, the author shows how this problem is related to the perturbed reversible 1-1 resonance vector fields, and allows its study to be completed.
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