- 02-21 V. Gelfreich
- Chaotic zone in the Bogdanov-Takens bifurcation for diffeomorphisms
Jan 15, 02
(auto. generated ps),
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Abstract. We consider a two-parametric analytic family of diffeomorphisms
near the Bogdanov-Takens bifurcation. It is known that if the
parameters belong to a homoclinic zone, the map has homoclinic points.
The width of the homoclinic zone is exponentially small.
We derive an asymptotic formula for the width of the homoclinic zone.
An analytic invariant associated with a parabolic fixed point
is an important ingredient of this formula. The proof of the asymptotic
formula is not complete. Additionally we provide results of
computations of the invariant for model families.