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.
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Gelfreich, V. (2003). Chaotic Zone in the Bogdanov-Takens Bifurcation for Diffeomorphisms. In: Begehr, H.G.W., Gilbert, R.P., Wong, M.W. (eds) Analysis and Applications — ISAAC 2001. International Society for Analysis, Applications and Computation, vol 10. Springer, Boston, MA. https://doi.org/10.1007/978-1-4757-3741-7_14
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DOI: https://doi.org/10.1007/978-1-4757-3741-7_14
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