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arXiv · 1802.00466

Local dynamics of parabolic skew-products

Liz Vivas
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Abstract

The local dynamics around a fixed point has been extensively studied for germs of one and several complex variables. In one dimension, there exist a complete picture of the trajectory of the orbits on a whole neighborhood of the fixed point. In dimensions larger or equal than two some partial results are known. In this article we analyze a case that lies in the boundary between one and several complex variables. We consider skew product maps of the form F (z, w) = ({\lambda}(z), f (z, w)). We deal with the case of parabolic skew product maps, that is when DF(0,0) = Id. Our goal is to describe the behavior of orbits around a whole neighborhood of the origin. We establish formulas for conjugacy maps in different regions of a neighborhood of the origin.

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Liz Vivas. 2018-02-01. Local dynamics of parabolic skew-products. https://arxiv.org/abs/1802.00466

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