Iterative Roots of Multifunctions
Dynamical Systems
2022-12-13 v1 Analysis of PDEs
Combinatorics
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.
Keywords
Cite
@article{arxiv.2212.05305,
title = {Iterative Roots of Multifunctions},
author = {B. V. Rajarama Bhat and Chaitanya Gopalakrishna},
journal= {arXiv preprint arXiv:2212.05305},
year = {2022}
}
Comments
16 pages, 8 figures