Homoclinic Orbits and Lagrangian Embeddings
| dc.creator | Lisi, Samuel T. | |
| dc.date | 2006-08-31 | |
| dc.date | 2007-08-12 | |
| dc.date.accessioned | 2026-07-07T08:22:59Z | |
| dc.date.available | 2026-07-07T08:22:59Z | |
| dc.description | This paper introduces techniques of symplectic topology to the study of homoclinic orbits in Hamiltonian systems. The main result is a strong generalization of homoclinic existence results due to Sere and to Coti-Zelati, Ekeland and Sere, which were obtained by variational methods. Our existence result uses a modification of a construction due to Mohnke (originally in the context of Legendrian chords), and an energy--capacity inequality of Chekanov. In essence, we show the existence of a homoclinic orbit by showing a certain Lagrangian embedding cannot exist. We consider a (possibly time dependent) Hamiltonian system on an exact symplectic manifold (W, ω= d λ) with a hyperbolic rest point. In the case of periodic time dependence, we show the existence of an orbit homoclinic to the rest point if λ(X_H) - H is positive and proper, H is positive outside a compact set and proper, and (W, ω) admits the structure of a Weinstein domain. In the autonomous case, we establish the existence of an orbit homoclinic to the rest point if the critical level is of restricted contact-type, and the critical level has a Hamiltonian displaceable neighbourhood. | |
| dc.description | 12 pages; fixed an error, provided more details, reorganized exposition of proof of Theorem 1.2 | |
| dc.identifier | https://arxiv.org/abs/math/0608801 | |
| dc.identifier | http://arxiv.org/abs/math/0608801 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/135840 | |
| dc.subject | Symplectic Geometry | |
| dc.subject | Dynamical Systems | |
| dc.subject | 37J45 (Primary); 53D12 (Secondary) | |
| dc.title | Homoclinic Orbits and Lagrangian Embeddings | |
| dc.type | text |