The gluing bifurcation: I. Symbolic dynamics of closed curves
- 1 February 1988
- journal article
- Published by IOP Publishing in Nonlinearity
- Vol. 1 (1), 203-214
- https://doi.org/10.1088/0951-7715/1/1/008
Abstract
The authors study the periodic orbits which can occur in a neighbourhood of a codimension-two gluing bifurcation involving two trajectories bi-asymptotic to the same stationary point. Provided some simple conditions are satisfied they prove that there are either zero, one or two closed curves and that these have a specific symbolic form which, in particular, allows them to associate a rotation number with each of them. Furthermore, pairs of orbits which can coexist are identified: the two rotation numbers must be Farey neighbours.Keywords
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