QUANTITATIVE DESTRUCTION AND PERSISTENCE OF LAGRANGIAN TORUS IN HAMILTONIAN SYSTEMS

Lin Wang

doi:10.3934/dcds.2026164

QUANTITATIVE DESTRUCTION AND PERSISTENCE OF LAGRANGIAN TORUS IN HAMILTONIAN SYSTEMS

Lin Wang^*

^*Corresponding author for this work

Beijing Institute of Technology

Research output: Contribution to journal › Article › peer-review

Abstract

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 C^r 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].

Original language	English
Pages (from-to)	203-225
Number of pages	23
Journal	Discrete and Continuous Dynamical Systems- Series A
Volume	59
DOIs	https://doi.org/10.3934/dcds.2026164
Publication status	Published - Feb 2027
Externally published	Yes

Keywords

hamiltonian systems
Lagrangian tori
trigonometric polynomials

Access to Document

10.3934/dcds.2026164

Cite this

@article{c5a4bc2f1b3e451980fa0f7c401c8180,

title = "QUANTITATIVE DESTRUCTION AND PERSISTENCE OF LAGRANGIAN TORUS IN HAMILTONIAN SYSTEMS",

abstract = "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].",

keywords = "hamiltonian systems, Lagrangian tori, trigonometric polynomials",

author = "Lin Wang",

year = "2027",

month = feb,

doi = "10.3934/dcds.2026164",

language = "English",

volume = "59",

pages = "203--225",

journal = "Discrete and Continuous Dynamical Systems- Series A",

issn = "1078-0947",

}

TY - JOUR

T1 - QUANTITATIVE DESTRUCTION AND PERSISTENCE OF LAGRANGIAN TORUS IN HAMILTONIAN SYSTEMS

AU - Wang, Lin

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 -

QUANTITATIVE DESTRUCTION AND PERSISTENCE OF LAGRANGIAN TORUS IN HAMILTONIAN SYSTEMS

Abstract

Keywords

Access to Document

Other files and links

Fingerprint

Cite this