A note on Hilbert 16th problem
Let H(n) be the maximum number of limit cycles that a planar polynomial vector field of degree n can have. In this paper we prove that H(n) is realizable by structurally stable vector fields with only hyperbolic limit cycles and that it is a strictly increasing function whenever it is finite.
| Authors: | , |
|---|---|
| Format: | article |
| Publication Date: | 2025 |
| Country: | España |
| Institution: | Universitat Autònoma de Barcelona |
| Repository: | Dipòsit Digital de Documents de la UAB |
| Language: | English |
| OAI Identifier: | oai:ddd.uab.cat:309367 |
| Online Access: | https://ddd.uab.cat/record/309367 https://dx.doi.org/urn:doi:10.1090/proc/17116 |
| Access Level: | Open access |
| Keyword: | Hilbert 16th problem Limit cycles Structurally stable vector fields |
| Summary: | Let H(n) be the maximum number of limit cycles that a planar polynomial vector field of degree n can have. In this paper we prove that H(n) is realizable by structurally stable vector fields with only hyperbolic limit cycles and that it is a strictly increasing function whenever it is finite. |
|---|