A counterexample to the "composition conjecture"
F. Pakovich
TL;DR
This paper presents a counterexample to the longstanding composition conjecture related to the infinitesimal center problem in polynomial Abel equations, challenging previous assumptions in the field.
Contribution
It introduces a specific class of counterexamples that disprove the composition conjecture in the context of polynomial Abel equations.
Findings
Counterexamples invalidate the composition conjecture.
The results impact the understanding of the center problem.
New insights into polynomial Abel equations are provided.
Abstract
In this note we construct a class of counterexamples to the "composition conjecture" concerning an infinitesimal version of the center problem for the polynomial Abel equation in the complex domain.
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 Algebra and Logic · Advanced Topics in Algebra · semigroups and automata theory