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Resonance regions for families of torus maps. (English) Zbl 0678.58034
A resonance region for a family of torus maps is the set of parameter values for which there exists a periodic orbit with a given rotation vector. For generic periodic families, resonance regions are projections of multiply connected manifolds. Numerical studies of the case $$n=2$$ illustrate the complicated internal bifurcation structure of the resonance regions. Codimension two bifurcation and transversal homoclinic orbits are shown to exist.
Reviewer: D.Zhang

##### MSC:
 37G99 Local and nonlocal bifurcation theory for dynamical systems
##### Keywords:
resonance region; periodic orbit; bifurcation; homoclinic orbits
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