A Quasi-Periodic Poincaré's Theorem

Files
99-345.pdf (372.05 KB)
Author(s)
Li, Yong
Yi, Yingfei
Advisor(s)
Editor(s)
Associated Organization(s)
Organizational Unit
Organizational Unit
Series
Collections
Research Publications
Supplementary to:
Permanent Link
http://hdl.handle.net/1853/29496
Abstract
We study the persistence of invariant tori on resonant surfaces of a nearly integrable Hamiltonian system under the usual Kolmogorov non-degenerate condition. By introducing a quasi-linear iterative scheme to deal with small divisors, we generalize the Poincaré theorem on the maximal resonance case (i.e., the periodic case) to the general resonance case (i.e., the quasi-periodic case) by showing the persistence of majority of invariant tori associated to non-degenerate relative equilibria on any resonant surface.
Sponsor
The first author was partially supported by NSFC grant 19971042, the National 973 Project of China: Nonlinearity, and the outstanding youth project of the Ministry of Education of China. The second author was partially supported by NSF grant DMS9803581.
Date
1999
Extent
Resource Type
Text
Resource Subtype
Pre-print
Rights Statement
Rights URI