Degenerate bifurcation points of periodic solutions of autonomous Hamiltonian systems
| dc.creator | Radzki, W. | |
| dc.creator | Rybicki, S. | |
| dc.date | 2006-04-12 | |
| dc.date.accessioned | 2026-07-07T07:10:51Z | |
| dc.date.available | 2026-07-07T07:10:51Z | |
| dc.description | We study connected branches of non-constant {$2π$-pe}riodic solutions of the Hamilton equation \begin{displaymath} \dot{x}(t)=λJ\nabla H(x(t)), \end{displaymath} where $λ\in\halfline,$ $H\in C^2(\R^n\times\R^n,\R)$ and $ \displaystyle \nabla^2H(x_0)= [ \begin{array}{cc} A&0 0&B \end{array} ] $ for $x_0\in\nabla H^{-1}(0).$ The Hessian $\nabla^2H(x_0)$ can be singular. We formulate sufficient conditions for the existence of such branches bifurcating from given $(x_0,λ_0).$ As a consequence we prove theorems concerning the existence of connected branches of arbitrary periodic nonstationary trajectories of the Hamiltonian system $\dot{x}(t)=J\nabla H(x(t))$ emanating from $x_0.$ We describe also minimal periods of trajectories near $x_0.$ | |
| dc.description | 18 pages | |
| dc.identifier | https://arxiv.org/abs/math/0604288 | |
| dc.identifier | http://arxiv.org/abs/math/0604288 | |
| dc.identifier | Journal of Differential Equations 202(2) (2004), 284-305 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/111550 | |
| dc.subject | Classical Analysis and ODEs | |
| dc.subject | 34C23, 34C25, 58F14, 70H05 | |
| dc.title | Degenerate bifurcation points of periodic solutions of autonomous Hamiltonian systems | |
| dc.type | text |