Iterative Roots of Multifunctions

2022/12/10 by Bhat, B. V. Rajarama, Gopalakrishna, Chaitanya
#05C20 #39B12 #54C60 #Analysis of PDEs (math.AP) #Combinatorics (math.CO) #Dynamical Systems (math.DS) #FOS: Mathematics

paper · doi:10.48550/arxiv.2212.05305

Abstract

Some easily verifiable sufficient conditions for the nonexistence of iterative roots for multifunctions on arbitrary nonempty sets are presented. Typically if the graph of the multifunction has a distinguished point with a relatively large number of paths leading to it then such a multifunction does not admit any iterative root. These results can be applied to single-valued maps by considering their pullbacks as multifunctions. This has been illustrated by showing the nonexistence of iterative roots of some specified orders for certain complex polynomials.

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