1988/02/01 by J M Gambaudo, J. M. Gambaudo, Paul Glendinning +3 · 1 citation
Mathematics · Physics and Astronomy · #Chaos control and synchronization #Mathematical Dynamics and Fractals #Quantum chaos and dynamical systems
paper · doi:10.1088/0951-7715/1/1/008
openalex publication_date 1988/02/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/30
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.