Existence of KAM tori for presymplectic vector fields
| dc.contributor.author | Bauer, Sean | |
| dc.contributor.author | Petrov, Nikola | |
| dc.date.accessioned | 2021-10-11T21:14:17Z | |
| dc.date.available | 2021-10-11T21:14:17Z | |
| dc.date.issued | 2020-12-22 | |
| dc.description.abstract | We prove the existence of a torus that is invariant with respect to the flow of a vector field that preserves the presymplectic form in an exact presymplectic manifold. The flow on this invariant torus is conjugate to a linear flow on a torus with a Diophantine velocity vector. The proof has an "a posteriori" format, the the invariant torus is constructed by using a Newton method in a space of functions, starting from a torus that is approximately invariant. The geometry of the problem plays a major role in the construction by allowing us to construct a special adapted basis in which the equations that need to be solved in each step of the iteration have a simple structure. In contrast to the classical methods of proof, this method does not assume that the system is close to integrable, and does not rely on using action-angle variables. | |
| dc.description.department | Mathematics | |
| dc.format | Text | |
| dc.format.extent | 26 pages | |
| dc.format.medium | 1 file (.pdf) | |
| dc.identifier.citation | Bauer, S., & Petrov, N. P. (2020). Existence of KAM tori for presymplectic vector fields. <i>Electronic Journal of Differential Equations, 2020</i>(126), pp. 1-26. | |
| dc.identifier.issn | 1072-6691 | |
| dc.identifier.uri | https://hdl.handle.net/10877/14636 | |
| dc.language.iso | en | |
| dc.publisher | 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, 2020, San Marcos, Texas: Texas State University and University of North Texas. | |
| dc.subject | KAM theory | |
| dc.subject | Invariant torus | |
| dc.subject | Presymplectic manifold | |
| dc.subject | Stability | |
| dc.title | Existence of KAM tori for presymplectic vector fields | |
| dc.type | Article |