Clustering Polar Curves
arXiv (Cornell University)(2021)
Abstract
This essay builds on the idea of grouping the polar curves of 2-variable function germs in polar clusters. One first obtains a bijective correspondence between certain partitions of the set of polar quotients of two topologically equivalent function germs. We explain how this bijective correspondence may be refined in the Lipschitz category in terms of the associated gradient canyons.
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Key words
Topological equivalence of functions,Polar curves,Lipschitz invariants
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