Rational solutions and limit cycles of polynomial and trigonometric Abel equations
Fuente:
arXiv
Salvato in:
| Autore principale: | |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2026
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866908855794925568 |
|---|---|
| author | Calderon, Luis Angel |
| author_facet | Calderon, Luis Angel |
| contents | We study the Abel differential equation x0 = A(t)x3 + B(t)x2 +C(t)x. Specifically, we find bounds on the number of its rational solutions when A(t), B(t) and C(t) are polynomials with real or complex coefficients; and on the number of rational limit cycles when A(t), B(t) and C(t) are trigonometric polynomials with real coefficients. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_23902 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Rational solutions and limit cycles of polynomial and trigonometric Abel equations Calderon, Luis Angel Classical Analysis and ODEs We study the Abel differential equation x0 = A(t)x3 + B(t)x2 +C(t)x. Specifically, we find bounds on the number of its rational solutions when A(t), B(t) and C(t) are polynomials with real or complex coefficients; and on the number of rational limit cycles when A(t), B(t) and C(t) are trigonometric polynomials with real coefficients. |
| title | Rational solutions and limit cycles of polynomial and trigonometric Abel equations |
| topic | Classical Analysis and ODEs |
| url | https://arxiv.org/abs/2602.23902 |