On minimal Rolle's domains for complex polynomials
Michael J. Miller
TL;DR
This paper investigates the properties and characteristics of minimal Rolle's domains, which are subsets of the complex plane containing critical points of certain complex polynomials, to understand their structure and minimality.
Contribution
It provides a detailed analysis of minimal Rolle's domains for complex polynomials, establishing foundational properties and conditions for their minimality.
Findings
Characterization of minimal Rolle's domains
Conditions for minimality of Rolle's domains
Insights into the structure of critical points in complex polynomials
Abstract
Define a subset of the complex plane to be a Rolle's domain if it contains (at least) one critical point of every complex polynomial P such that P(-1)=P(1). Define a Rolle's domain to be minimal if no proper subset is a Rolle's domain. In this paper, we investigate minimal Rolle's domains.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsAdvanced Differential Equations and Dynamical Systems · Mathematical Dynamics and Fractals · Meromorphic and Entire Functions