ON THE EXISTENCE OF KAM TORI FOR PRESYMPLECTIC VECTOR FIELDS

Bauer, Sean

ON THE EXISTENCE OF KAM TORI FOR PRESYMPLECTIC VECTOR FIELDS

dc.contributor.advisor	Petrov, Nikola
dc.contributor.author	Bauer, Sean
dc.contributor.committeeMember	Grasse, Kevin
dc.contributor.committeeMember	Grigo, Alex
dc.contributor.committeeMember	Lakshmivarahan, S
dc.contributor.committeeMember	Remling, Christian
dc.date.accessioned	2016-05-18T15:34:56Z
dc.date.available	2016-05-18T15:34:56Z
dc.date.issued	2016-05
dc.date.manuscript	2016-05
dc.description.abstract	We prove the existence of a torus that is invariant with respect to the flow of a presymplectic vector field found in a family of presymplectic vector fields. Moreover, the flow on this invariant torus is conjugate to a linear flow on a torus with a Diophantine velocity vector. This torus is constructed by iteratively solving functional equations using a Newton method in a space of functions by starting from a torus that is approximately invariant. 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. The geometry of the problem is used to simplify the equations that come from the Newton method. This method of proof can be implemented into efficient numerical algorithms.	en_US
dc.identifier.uri	http://hdl.handle.net/11244/34745
dc.language	en	en_US
dc.subject	Dynamical Systems	en_US
dc.subject	Presymplectic	en_US
dc.subject	KAM	en_US
dc.thesis.degree	Ph.D.	en_US
dc.title	ON THE EXISTENCE OF KAM TORI FOR PRESYMPLECTIC VECTOR FIELDS	en_US
ou.group	College of Arts and Sciences::Department of Mathematics	en_US