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Splitting of a small separatrix loop near the saddle-center bifurcation in area-preserving maps. (English) Zbl 0942.37016

The author deals with the splitting of a small separatrix loop that appears after the Bogdanov-Takens (saddle-center) bifurcation in an analytic family of area-preserving maps and proves that in general the splitting is described by almost the “same formula” as in the case of the standard map. More precisely, the author derives an asymptotic formula that describes the splitting, and studies the properties of the pre-exponential factor.

MSC:

37D30 Partially hyperbolic systems and dominated splittings
37D45 Strange attractors, chaotic dynamics of systems with hyperbolic behavior
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