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Local dynamics of parabolic skew-products. (arXiv:1802.00466v1 [math.CV])
来源于:arXiv
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. 查看全文>>