Higher Order Branching of Periodic Orbits from Polynomial Isochrones
| dc.contributor.author | Toni, Bourama | |
| dc.date.accessioned | 2019-11-22T18:04:34Z | |
| dc.date.available | 2019-11-22T18:04:34Z | |
| dc.date.issued | 1999-09-20 | |
| dc.description.abstract | We discuss the higher order local bifurcations of limit cycles from polynomial isochrones (linearizable centers) when the linearizing transformation is explicitly known and yields a polynomial perturbation one-form. Using a method based on the relative cohomology decomposition of polynomial one-forms complemented with a step reduction process, we give an explicit formula for the overall upper bound of branch points of limit cycles in an arbitrary <i>n</i> degree polynomial perturbation of the linear isochrone, and provide an algorithmic procedure to compute the upper bound at successive orders. We derive a complete analysis of the nonlinear cubic Hamiltonian isochrone and show that at most nine branch points of limit cycles can bifurcate in a cubic polynomial perturbation. Moreover, perturbations with exactly two, three, four, six, and nine local families of limit cycles may be constructed. | |
| dc.description.department | Mathematics | |
| dc.format | Text | |
| dc.format.extent | 15 pages | |
| dc.format.medium | 1 file (.pdf) | |
| dc.identifier.citation | Toni, B. (1999). Higher order branching of periodic orbits from polynomial isochrones. <i>Electronic Journal of Differential Equations, 1999</i>(35), pp. 1-15. | |
| dc.identifier.issn | 1072-6691 | |
| dc.identifier.uri | https://hdl.handle.net/10877/8880 | |
| dc.language.iso | en | |
| dc.publisher | Southwest Texas State University, Department of Mathematics | |
| dc.rights | Attribution 4.0 International | |
| dc.rights.uri | https://creativecommons.org/licenses/by/4.0/ | |
| dc.source | Electronic Journal of Differential Equations, 1999, San Marcos, Texas: Southwest Texas State University and University of North Texas. | |
| dc.subject | Limit cycles | |
| dc.subject | Isochrones | |
| dc.subject | Perturbations | |
| dc.subject | Cohomology decomposition | |
| dc.title | Higher Order Branching of Periodic Orbits from Polynomial Isochrones | |
| dc.type | Article |