On the existence and construction of Dulac functions
Osuna Osvaldo, Rodr\'iguez-Ceballos Joel, Vargas-De-Le\'on Cruz,, Villase\~nor-Aguilar Gabriel
TL;DR
This paper establishes conditions under which Dulac functions exist for certain vector fields, providing methods for their construction and illustrating the results with applications and examples.
Contribution
It introduces new sufficient conditions for the existence of Dulac functions based on the components of vector fields, along with construction techniques.
Findings
Sufficient conditions for Dulac function existence
Construction methods for Dulac functions
Applications demonstrating the results
Abstract
We provide sufficient conditions on the components of a vector field, which ensure the existence of Dulac functions depending on special functions for such vector field. We also present some applications and examples in order to illustrate our results.
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 · Meromorphic and Entire Functions · Nonlinear Waves and Solitons