TY - JOUR
T1 - QUANTITATIVE DESTRUCTION AND PERSISTENCE OF LAGRANGIAN TORUS IN HAMILTONIAN SYSTEMS
AU - Wang, Lin
N1 - Publisher Copyright:
© 2026, American Institute of Mathematical Sciences. All rights reserved.
PY - 2027/2
Y1 - 2027/2
N2 - For an integrable Hamiltonian system with d degrees of freedom (d≥ 2), we quantitatively investigate the existence and non-existence of flow-invariant Lagrangian tori with a given frequency under perturbations lying beyond the reach of the classical KAM theory in the Cr topology. As an application, for nearly integrable Hamiltonian systems where the perturbations are restricted to trigonometric polynomials, the non-existence result provides a partial answer to an open problem in the same spirit as converse KAM, posed by Mather in 1988 [27; p. 212].
AB - For an integrable Hamiltonian system with d degrees of freedom (d≥ 2), we quantitatively investigate the existence and non-existence of flow-invariant Lagrangian tori with a given frequency under perturbations lying beyond the reach of the classical KAM theory in the Cr topology. As an application, for nearly integrable Hamiltonian systems where the perturbations are restricted to trigonometric polynomials, the non-existence result provides a partial answer to an open problem in the same spirit as converse KAM, posed by Mather in 1988 [27; p. 212].
KW - hamiltonian systems
KW - Lagrangian tori
KW - trigonometric polynomials
UR - https://www.scopus.com/pages/publications/105051085791
U2 - 10.3934/dcds.2026164
DO - 10.3934/dcds.2026164
M3 - Article
AN - SCOPUS:105051085791
SN - 1078-0947
VL - 59
SP - 203
EP - 225
JO - Discrete and Continuous Dynamical Systems- Series A
JF - Discrete and Continuous Dynamical Systems- Series A
ER -