ARNOLD-TYPE THEOREM ABOUT LOWER-DIMENSIONAL INVARIANT TORI IN GENERALIZED HAMILTONIAN SYSTEMS

Jiayin Du

doi:10.11948/20220236

2022 Volume 12 Issue 6

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Article navigation > Journal of Applied Analysis & Computation > 2022 > 12(6): 2621-2639

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Jiayin Du. ARNOLD-TYPE THEOREM ABOUT LOWER-DIMENSIONAL INVARIANT TORI IN GENERALIZED HAMILTONIAN SYSTEMS[J]. Journal of Applied Analysis & Computation, 2022, 12(6): 2621-2639. doi: 10.11948/20220236

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Jiayin Du. ARNOLD-TYPE THEOREM ABOUT LOWER-DIMENSIONAL INVARIANT TORI IN GENERALIZED HAMILTONIAN SYSTEMS[J]. Journal of Applied Analysis & Computation, 2022, 12(6): 2621-2639. doi: 10.11948/20220236

ARNOLD-TYPE THEOREM ABOUT LOWER-DIMENSIONAL INVARIANT TORI IN GENERALIZED HAMILTONIAN SYSTEMS

Jiayin Du

College of Mathematics, Jilin University, Changchun 130012, China

Author Bio: Email: dujy20@mails.jlu.edu.cn(J. Du)

Abstract

Abstract

In this paper, we consider the lower dimensional invariant tori for generalized Hamiltonian system. A so-called generalized Hamiltonian system is defined on a Poisson manifold which can be odd dimensional and structurally degenerate. The existence of quasi-periodic invariant tori for Hamiltonian with standard symplectic structure was first shown by Arnold [2] under a degeneracy-removing condition. We prove the persistence of lower dimensional tori for Hamiltonian with Poisson structure instead of standard symplectic structure, when the tangential and normal frequencies satisfy some certain conditions.
- KAM theory /
- generalized Hamiltonian system /
- Arnold-type theorem /
- lower-dimensional tori
MSC: 37J40, 70H08

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References

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