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báo cáo hóa học:" Research Article On Invariant Tori of Nearly Integrable Hamiltonian Systems with Quasiperiodic Perturbation"

Tuyển tập báo cáo các nghiên cứu khoa học quốc tế ngành hóa học dành cho các bạn yêu hóa học tham khảo đề tài: Research Article On Invariant Tori of Nearly Integrable Hamiltonian Systems with Quasiperiodic Perturbation | Hindawi Publishing Corporation Fixed Point Theory and Applications Volume 2010 Article ID 697343 17 pages doi 10.1155 2010 697343 Research Article On Invariant Tori of Nearly Integrable Hamiltonian Systems with Quasiperiodic Perturbation Dongfeng Zhang1 and Rong Cheng2 1 Department of Mathematics Southeast University Nanjing 210096 China 2 College of Mathematics and Physics Nanjing University of Information Science and Technology Nanjing 210044 China Correspondence should be addressed to Dongfeng Zhang zhdf@seu.edu.cn Received 2 September 2010 Accepted 25 October 2010 Academic Editor Marlene Frigon Copyright 2010 D. Zhang and R. Cheng. This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited. We are concerned with the persistence of frequency of invariant tori for analytic integrable Hamiltonian system with quasiperiodic perturbation. It is proved that if the unperturbed system satisfies the Russmann s nondegeneracy condition and has nonzero Brouwer s topological degree at some Diophantine frequency the perturbed system satisfies the colinked nonresonant condition then the invariant torus with this frequency persists under quasiperiodic perturbation. 1. Introduction and Main Results It is well known that the classical KAM theorem concludes that most of invariant tori of integrable Hamiltonian system can survive small perturbation under Kolmogorov s nondegeneracy condition 1-4 . What is more the frequency of the persisting invariant tori remains the same. Later important generalizations of the classical KAM theorem were made to the Russmann s nondegeneracy condition 5-9 . However in the case of Russmann s nondegeneracy condition we can only get the existence of a family of invariant tori while there is no information on the persistence of frequency of any torus. Recently Chow et al. 10 and Sevryuk 11 consider .