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Journal articles on the topic 'Kolmogorov-Arnold-Moser Theorem'

Author: Grafiati

Published: 4 June 2021

Last updated: 28 July 2025

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1

Rangarajan, Govindan. "Kolmogorov-Arnold-Moser theorem." Resonance 3, no. 4 (1998): 43–53. http://dx.doi.org/10.1007/bf02834611.

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2

Lou, Zhaowei, and Yingnan Sun. "A KAM theorem for higher dimensional reversible nonlinear Schrodinger equations." Electronic Journal of Differential Equations 2022, no. 01-87 (2022): 69. http://dx.doi.org/10.58997/ejde.2022.69.

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In this article we prove an abstract Kolmogorov-Arnold-Moser (KAM) theorem for infinite dimensional reversible systems. Using this theorem, we obtain the existence of quasi-periodic solutions for a class of reversible (non-Hamiltonian) coupled nonlinear Schrodinger systems on a d-torus.

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3

Khesin, Boris, and Sergei Tabachnikov. "Vladimir Igorevich Arnold. 12 June 1937—3 June 2010." Biographical Memoirs of Fellows of the Royal Society 64 (August 30, 2017): 7–26. http://dx.doi.org/10.1098/rsbm.2017.0016.

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Vladimir Arnold was a pre-eminent mathematician of the second half of the twentieth and early twenty-first century. Kolmogorov–Arnold–Moser (KAM) theory, Arnold diffusion, Arnold tongues in bifurcation theory, Liouville–Arnold theorem in completely integrable systems, Arnold conjectures in symplectic topology—this is a very incomplete list of notions and results named after him. Arnold was a charismatic leader of a mathematical school, a prolific writer, a flamboyant speaker and a tremendously erudite person. Our biographical sketch describes his extraordinary personality and his major contrib

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4

TASSO, H., and G. N. THROUMOULOPOULOS. "On the existence of resistive magnetohydrodynamic equilibria." Journal of Plasma Physics 73, no. 3 (2007): 285–87. http://dx.doi.org/10.1017/s002237780700637x.

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AbstractA necessary condition for the existence of general dissipative magneto-hydrodynamic equilibria is derived. The derivation comprises Ohm's law and the existence of magnetic surfaces, only in the sense of the Kolmogorov–Arnold–Moser (KAM) theorem. All other equations describing the system are only required for evaluating the condition for a specific case.

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5

Lou, Zhaowei, and Youchao Wu. "KAM theorem for degenerate infinite-dimensional reversible systems." Electronic Journal of Differential Equations 2024, no. 01-?? (2024): 02. http://dx.doi.org/10.58997/ejde.2024.02.

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In this article, we establish a Kolmogorov-Arnold-Moser (KAM) theorem for degenerate infinite-dimensional reversible systems under a non-degenerate condition of Russmann type. This theorem broadens the scope of applicability of degenerate KAM theory, previously confined to Hamiltonian systems, by incorporating infinite-dimensional reversible systems. Using this theorem, we obtain the existence and linear stability of quasi-periodic solutions for a class of non-Hamiltonian but reversible beam equations with non-linearities in derivatives. For more information see https://ejde.math.txstate.edu/V

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6

Rui, Jie, Min Zhang, and Yi Wang. "Kolmogorov–Arnold–Moser theorem for nonlinear beam equations with almost-periodic forcing." Journal of Mathematical Analysis and Applications 493, no. 2 (2021): 124529. http://dx.doi.org/10.1016/j.jmaa.2020.124529.

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7

Zhang, Min, Yi Wang, and Jie Rui. "Quasi-periodic solutions for one dimensional Schrödinger equation with quasi-periodic forcing and Dirichlet boundary condition." Journal of Mathematical Physics 64, no. 1 (2023): 011509. http://dx.doi.org/10.1063/5.0093668.

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This paper is concerned with a one-dimensional quasi-periodically forced nonlinear Schrödinger equation under Dirichlet boundary conditions. The existence of the quasi-periodic solutions for the equation is verified. By infinitely many symplectic transformations of coordinates, the Hamiltonian of the linear part of the equation can be reduced to an autonomous system. By utilizing the measure estimation of small divisors, there exists a symplectic change of coordinate transformation of the Hamiltonian of the equation into a nice Birkhoff normal form. By an abstract KAM (Kolmogorov-Arnold-Moser)

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8

Lin, W. A., and L. E. Reichl. "Spectral analysis of quantum-resonance zones, quantum Kolmogorov-Arnold-Moser theorem, and quantum-resonance overlap." Physical Review A 37, no. 10 (1988): 3972–85. http://dx.doi.org/10.1103/physreva.37.3972.

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9

Wiggins, S., and A. M. Mancho. "Barriers to transport in aperiodically time-dependent two-dimensional velocity fields: Nekhoroshev's theorem and "Nearly Invariant" tori." Nonlinear Processes in Geophysics 21, no. 1 (2014): 165–85. http://dx.doi.org/10.5194/npg-21-165-2014.

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Abstract. In this paper we consider fluid transport in two-dimensional flows from the dynamical systems point of view, with the focus on elliptic behaviour and aperiodic and finite time dependence. We give an overview of previous work on general nonautonomous and finite time vector fields with the purpose of bringing to the attention of those working on fluid transport from the dynamical systems point of view a body of work that is extremely relevant, but appears not to be so well known. We then focus on the Kolmogorov–Arnold–Moser (KAM) theorem and the Nekhoroshev theorem. While there is no f

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10

Chandre, C., and H. R. Jauslin. "A version of Thirring’s approach to the Kolmogorov–Arnold–Moser theorem for quadratic Hamiltonians with degenerate twist." Journal of Mathematical Physics 39, no. 11 (1998): 5856–65. http://dx.doi.org/10.1063/1.532599.

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11

Aldonin, Gennady, and Vasiliy Cherepanov. "Model of the Process of Self-Organization of the Heart Rhythm." Infocommunications and Radio Technologies 5, no. 4 (2022): 472–83. http://dx.doi.org/10.29039/2587-9936.2022.05.4.35.

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The paper considers a synergistic analysis of the physical and physiological nature of electrical processes in the human heart, namely in the most important biosystem – the conduction nervous system of the heart (CNSH), in particular, the heart pacemaker. Currently, promising methods for studying CNSH as an active medium are being actively developed, using the foundations of nonlinear dynamics. Methods for describing active media are widely used in the study of the phenomena of the work of the heart pacemaker, where the active medium is represented as an ensemble of some elements that locally

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12

Scott, Chris, and Andras Kovacs. "The elementary charge value might be determined by Hamiltonian dynamics." Journal of Physics: Conference Series 2987, no. 1 (2025): 012013. https://doi.org/10.1088/1742-6596/2987/1/012013.

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Abstract With the electron’s discovery in 1897, it became recognized that each electron has exactly the same electric charge quantum, known as the elementary charge value. In natural units, the elementary charge value is the square root of the electromagnetic fine structure constant, which yields the ground state electron speed in the hydrogen atom. The origin of these fundamental constants has been a long-standing mystery ever since the electron’s discovery. We propose that the elementary charge value may be calculable via a Hamiltonian dynamics based method. Hamiltonian dynamics applies to t

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13

Zhang, Min, Zhe Hu, and Yonggang Chen. "Invariant Tori for a Two-Dimensional Completely Resonant Beam Equation with a Quintic Nonlinear Term." Journal of Function Spaces 2022 (October 5, 2022): 1–15. http://dx.doi.org/10.1155/2022/7106366.

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This paper focuses on a two-dimensional completely resonant beam equation with a quintic nonlinear term. This means studying u t t + Δ 2 u + ε f u = 0 , x ∈ T 2 , t ∈ ℝ , under periodic boundary conditions, where ε is a small positive parameter and f u is a real analytic odd function of the form f u = f 5 u 5 + ∑ i ^ ≥ 3 f 2 i ^ + 1 u 2 i ∧ + 1 , f 5 ≠ 0 . It is proved that the equation admits small-amplitude, Whitney smooth, linearly stable quasiperiodic solutions on the phase-flow invariant subspace ℤ † 2 = r = r 1 , r 2 , r 1 ∈ 4 ℤ − 1 , r 2 ∈ 4 ℤ . Firstly, the corresponding Hamiltonian sy

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14

Guan, Xinyu, and Nan Kang. "Stability for Cauchy problem of first order linear PDEs on $ \mathbb{T}^m $ with forced frequency possessing finite uniform Diophantine exponent." AIMS Mathematics 9, no. 7 (2024): 17795–826. http://dx.doi.org/10.3934/math.2024866.

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<abstract><p>In this paper, we studied the stability of the Cauchy problem for a class of first-order linear quasi-periodically forced PDEs on the $ m $-dimensional torus:</p> <p><disp-formula> <label/> <tex-math id="FE1"> \begin{document}$ \begin{eqnarray*} \left\{ \begin{array}{l} \partial_t u+(\xi+f(x, \omega t, \xi))\cdot \partial_x u = 0, \\ u(x, 0) = u_0(x), \ \end{array} \right. \end{eqnarray*} $\end{document} </tex-math></disp-formula></p> <p>where $ \xi\in \mathbb{R}^m, x\in \mathbb{T}^m, \omega\in\mathbb{R}^d, $ in the

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15

Xue, Shuaishuai, and Yingnan Sun. "KAM tori for two dimensional completely resonant derivative beam system." Journal of Mathematical Physics 65, no. 6 (2024). http://dx.doi.org/10.1063/5.0183958.

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In this paper, we introduce an abstract KAM (Kolmogorov–Arnold–Moser) theorem. As an application, we study the two-dimensional completely resonant beam system under periodic boundary conditions. Using the KAM theorem together with partial Birkhoff normal form method, we obtain a family of Whitney smooth small–amplitude quasi–periodic solutions for the equation system.

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16

Ge, Chuanfang, and Jiansheng Geng. "Quasi-periodic solutions for quintic completely resonant derivative beam equations on T2." Journal of Mathematical Physics 64, no. 9 (2023). http://dx.doi.org/10.1063/5.0154905.

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In the present paper, we consider two dimensional completely resonant, derivative, quintic nonlinear beam equations with reversible structure. Because of this reversible system without external parameters or potentials, Birkhoff normal form reduction is necessary before applying Kolmogorov–Arnold–Moser (KAM) theorem. As application of KAM theorem, the existence of partially hyperbolic, small amplitude, quasi-periodic solutions of the reversible system is proved in this paper.

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17

MacKay, Robert S. "Introduction to Arnold’s proof of the Kolmogorov–Arnold–Moser theorem." Contemporary Physics, August 22, 2024, 1–2. http://dx.doi.org/10.1080/00107514.2024.2386993.

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18

Singh, Bhawna, Sada Nand Prasad, and Abdullah. "Nonlinear stability in a new kind of Robe’s problem." Modern Physics Letters A, January 31, 2025. https://doi.org/10.1142/s0217732324502122.

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In the Robe’s restricted three-body problem, we have considered the motion of the test particle which is moving inside the outermost layer of the heterogeneous body. This heterogeneous body has N layers with different densities and is filled with viscous fluid. The test particle which is taken as the third (or infinitesimal) body is moving under the influence of the heterogeneous body (primary) and point mass (secondary). We are motivated from Ansari, 1 where the linear stability and other important properties of this specific model have been discussed. In this paper, we have extended their wo

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19

CAI, AO, HUIHUI LV, and ZHIGUO WANG. "Quantitative reducibility of ${\boldsymbol {C}^{\boldsymbol {k}}}$ quasi-periodic cocycles." Ergodic Theory and Dynamical Systems, November 13, 2024, 1–24. http://dx.doi.org/10.1017/etds.2024.88.

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Abstract This paper establishes an extreme $C^k$ reducibility theorem of quasi-periodic $SL(2, \mathbb {R})$ cocycles in the local perturbative region, revealing both the essence of Eliasson [Floquet solutions for the 1-dimensional quasi-periodic Schrödinger equation. Comm. Math. Phys.146 (1992), 447–482], and Hou and You [Almost reducibility and non-perturbative reducibility of quasi-periodic linear systems. Invent. Math.190 (2012), 209–260] in respectively the non-resonant and resonant cases. By paralleling further the reducibility process with the almost reducibility, we are able to acquire

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20

Li, Xuemei, and Yechi Liu. "Hopf and Double Hopf Bifurcations in a Delayed Lateral Vibration Model of Footbridges Induced by Pedestrians." International Journal of Bifurcation and Chaos, June 27, 2025. https://doi.org/10.1142/s0218127425501214.

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In this paper, we investigate the dynamical behaviors of a delayed lateral vibration model of footbridges. The model is proposed based on the facts that pedestrians will reduce their walking speeds or stop walking when the response of the footbridge becomes sufficiently large, and that the angular velocity of bridge vibration cannot be changed instantaneously when pedestrians begin to walk on the bridge. By analyzing the distribution of roots of the associated characteristic equation, we prove that there are only two types of bifurcations in this model: Hopf bifurcation and double Hopf bifurca

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21

Yu, Yi-Xiang, Jinwu Ye, Wu-Ming Liu, and CunLin Zhang. "Quantum analog of the Kolmogorov-Arnold-Moser theorem in the anisotropic Dicke model and its possible implications in the hybrid Sachdev-Ye-Kitaev models." Physical Review A 106, no. 2 (2022). http://dx.doi.org/10.1103/physreva.106.022213.

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22

Enciso, Alberto, Daniel Peralta-Salas, and Álvaro Romaniega. "Beltrami fields exhibit knots and chaos almost surely." Forum of Mathematics, Sigma 11 (2023). http://dx.doi.org/10.1017/fms.2023.52.

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Abstract In this paper, we show that, with probability $1$ , a random Beltrami field exhibits chaotic regions that coexist with invariant tori of complicated topologies. The motivation to consider this question, which arises in the study of stationary Euler flows in dimension 3, is V.I. Arnold’s 1965 speculation that a typical Beltrami field exhibits the same complexity as the restriction to an energy hypersurface of a generic Hamiltonian system with two degrees of freedom. The proof hinges on the obtention of asymptotic bounds for the number of horseshoes, zeros and knotted invariant tori and

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