JournalsjfgVol. 7, No. 1pp. 63–86

Interesting examples in C2\mathbb{C}^2 of maps tangent to the identity without domains of attraction

  • Sara Lapan

    University of California, Riverside, USA
Interesting examples in $\mathbb{C}^2$ of maps tangent to the identity without domains of attraction cover
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Abstract

We give an interesting example of a map in C2\mathbb{C}^2 that is tangent to the identity at the origin, but that does not have a domain of attraction along any of its characteristic directions at the origin. This map has three characteristic directions, two of which are not attracting while the third attracts points to that direction, but not to the origin. In addition, we show that if we add higher degree terms to this map, sometimes a domain of attraction along one of its characteristic directions will exist and sometimes one will not.

Cite this article

Sara Lapan, Interesting examples in C2\mathbb{C}^2 of maps tangent to the identity without domains of attraction. J. Fractal Geom. 7 (2020), no. 1, pp. 63–86

DOI 10.4171/JFG/84