Title:
The Cyclicity of Period Annulus of Degenerate Quadratic Hamiltonian System with Elliptic Segment
The Cyclicity of Period Annulus of Degenerate Quadratic Hamiltonian System with Elliptic Segment
dc.contributor.author | Chow, Shui-Nee | |
dc.contributor.author | Li, Chengzhi | |
dc.contributor.author | Yi, Yingfei | |
dc.contributor.corporatename | Georgia Institute of Technology. School of Mathematics | |
dc.contributor.corporatename | National University of Singapore. Dept. of Mathematics | |
dc.contributor.corporatename | Peking University. School of Mathematical Sciences | |
dc.date.accessioned | 2009-08-10T17:09:21Z | |
dc.date.available | 2009-08-10T17:09:21Z | |
dc.date.issued | 2000 | |
dc.description | AMS (MOS). Mathematics Subject Classification. 58F21, 34C05, 58F27, 58F30. | en |
dc.description.abstract | We study the cyclicity of period annuli (or annulus) for general degenerate quadratic Hamiltonian systems with an elliptic segment or a saddle loop, under quadratic perturbations. By using geometrical arguments and studying the respective Abelian integral based on the Picard-Fuchs equation, it is shown that the cyclicity of period annuli or annulus for such systems equals two. This result, together with those of [8],[10],[11],[18],[19], gives a complete solution to the infinitesimal Hilbert 16th problem in the case of degenerate quadratic Hamiltonian systems under quadratic perturbations. | en |
dc.identifier.uri | http://hdl.handle.net/1853/29492 | |
dc.language.iso | en_US | en |
dc.publisher | Georgia Institute of Technology | en |
dc.relation.ispartofseries | CDSNS2000-366 | en |
dc.subject | Abelian integral | en |
dc.subject | Cyclicity of period annulus | en |
dc.subject | Degenerate quadratic Hamiltonian system | en |
dc.subject | Infinitesimal Hilbert 16th problem | en |
dc.title | The Cyclicity of Period Annulus of Degenerate Quadratic Hamiltonian System with Elliptic Segment | en |
dc.type | Text | |
dc.type.genre | Pre-print | |
dspace.entity.type | Publication | |
local.contributor.author | Chow, Shui-Nee | |
local.contributor.corporatename | College of Sciences | |
local.contributor.corporatename | School of Mathematics | |
relation.isAuthorOfPublication | 184e1861-af72-4c62-b613-54c1d1b7febb | |
relation.isOrgUnitOfPublication | 85042be6-2d68-4e07-b384-e1f908fae48a | |
relation.isOrgUnitOfPublication | 84e5d930-8c17-4e24-96cc-63f5ab63da69 |