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arXiv · 1501.00244

Domain of attraction for maps tangent to the identity in $\mathbb{C}^2$ with characteristic direction of higher degree

Sara Lapan
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Abstract

We study holomorphic fixed point germs in two complex variables that are tangent to the identity and have a degenerate characteristic direction. We show that if that characteristic direction is also a characteristic direction for higher degree terms, is non-degenerate for a higher degree term, and satisfies some additional properties, then there is a domain of attraction on which points converge to the origin along that direction.

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Sara Lapan. 2015-01-01. Domain of attraction for maps tangent to the identity in $\mathbb{C}^2$ with characteristic direction of higher degree. https://doi.org/10.1007/s12220-015-9637-z

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