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A KAM Theorem for the Hamiltonian with Finite Zero Normal Frequencies and Its Applications (In Memory of Professor Walter Craig)
we investigate the existences of KAM tori for the infinite dimensional Hamiltonian system with finite number of zeros among normal frequencies. By...
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The KAM theorem with a large perturbation and application to the network of Duffing oscillators
We prove that there is an invariant torus with the given Diophantine frequency vector for a class of Hamiltonian systems defined by an integrable...
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Persistence of Hyperbolic-type Degenerate Lower-dimensional Invariant Tori with Prescribed Frequencies in Hamiltonian Systems
It is known that under Kolmogorov’s nondegeneracy condition, the nondegenerate hyperbolic invariant torus with Diophantine frequencies will persist...
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Accurate Computations up to Breakdown of Quasi-Periodic Attractors in the Dissipative Spin–Orbit Problem
We consider a Celestial Mechanics model: the spin–orbit problem with a dissipative tidal torque, which is a singular perturbation of a conservative...
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V. I. Arnold’s “Global” KAM Theorem and Geometric Measure Estimates
This paper continues the discussion started in [
10 ] concerning Arnold’s legacy on classical KAM theory and (some of) its modern developments.... -
Existence and Linear Stability of Symmetric Periodic Orbits in the Generalized Planar Stark–Zeeman Problem
The purpose of this paper is to demonstrate the existence of symmetric periodic solutions for a two-dimensional hydrogen atom subject to external...
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Persistence of Degenerate Lower Dimensional Invariant Tori with Prescribed Frequencies in Reversible Systems
This paper considers small perturbations of an integrable reversible system which has a degenerated lower dimensional invariant torus in some sense....
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KAM theory for the reversible perturbations of 2D linear beam equations
In the present paper, we prove an infinite dimensional reversible Kolmogorov-Arnold-Moser (KAM) theorem. As an application, we study the existence of...
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A KAM Theorem for the Time Quasi-periodic Reversible Perturbations of Linear Wave Equations Beyond Brjuno Conditions
This paper is concerned with the existence of quasi-periodic response solutions (i.e., solutions that are quasi-periodic with the same frequencies as...
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Rectifiability of divergence-free fields along invariant 2-tori
We find conditions under which the restriction of a divergence-free vector field B to an invariant toroidal surface S is rectifiable; namely constant...
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A KAM Theorem for Two Dimensional Completely Resonant Reversible Schrödinger Systems
In this paper, we prove an abstract KAM (Kolmogorov–Arnold–Moser) theorem for infinite dimensional reversible Schrödinger systems. Using this KAM...
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On the Stability of the Zero Solution of a Periodic Reversible Second-Order Differential Equation
AbstractThe problem concerning stability of the zero solution of a second-order differential equation describing the periodic perturbations of an...
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Quasi-periodic Solutions for Completely Resonant Quintic Beam Equations
This paper concerns the existence of quasi-periodic solutions for completely resonant quintic beam equations on one-dimensional tori. A novel...
