Relevant bibliographies by topics / Kolmogorov-Arnold-Moser Theorem

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  2. Dissertations / Theses
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Academic literature on the topic 'Kolmogorov-Arnold-Moser Theorem'

Author: Grafiati
Published: 4 June 2021
Last updated: 28 July 2025

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

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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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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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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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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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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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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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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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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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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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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Dissertations / Theses on the topic "Kolmogorov-Arnold-Moser Theorem"

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Huang, Yong-Shiang, and 黃詠翔. "On Kolmogorov-Arnold-Moser Theory." Thesis, 2014. http://ndltd.ncl.edu.tw/handle/54311972566643875331.

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碩士<br>國立清華大學<br>數學系<br>102<br>We will study two basic and important examples about circle diffeomorphisms and Hamiltonian systems, to clarify the central ideas of the celebrated Kolmogorov-Arnold-Moser Theory in perturbation theory. Two difficulties those pioneers encounter in early 20th century - problems of the small divisor and loss of differentiability, will be revealed and overcame in our procedures also.
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Books on the topic "Kolmogorov-Arnold-Moser Theorem"

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author, Kappeler Thomas 1953, and Montalto Riccardo author, eds. KAM tori for perturbations of the defocusing NLS equation. Société mathématique de France, 2018.

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Feldmeier, Achim. Introduction to Arnold's Proof of the Kolmogorov-Arnold-Moser Theorem. Taylor & Francis Group, 2022.

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Feldmeier, Achim. Introduction to Arnolds Proof of the Kolmogorov-Arnold-Moser Theorem. CRC Press LLC, 2022.

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Feldmeier, Achim. Introduction to Arnold's Proof of the Kolmogorov-Arnold-Moser Theorem. CRC Press LLC, 2022.

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Feldmeier, Achim. Introduction to Arnold's Proof of the Kolmogorov-Arnold-Moser Theorem. Taylor & Francis Group, 2022.

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Feldmeier, Achim. Introduction to Arnold's Proof of the Kolmogorov-Arnold-Moser Theorem. Taylor & Francis Group, 2022.

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Dumas, H. S. The KAM Story: A Friendly Introduction to the Content, History, and Significance of Classical Kolmogorov-Arnold-Moser Theory. World Scientific Publishing Company, 2014.

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Nolte, David D. From Butterflies to Hurricanes. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198805847.003.0009.

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Half a century after Poincaré first glimpsed chaos in the three-body problem, the great Russian mathematician Andrey Kolmogorov presented a sketch of a theorem that could prove that orbits are stable. In the hands of Vladimir Arnold and Jürgen Moser, this became the Kolmo–Arnol–Mos (KAM) theory of Hamiltonian chaos. This chapter shows how KAM theory fed into topology in the hands of Stephen Smale and helped launch the new field of chaos theory. Edward Lorenz discovered chaos in numerical models of atmospheric weather and discovered the eponymous strange attractor. Mathematical aspects of chaos
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Book chapters on the topic "Kolmogorov-Arnold-Moser Theorem"

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Mahnke, Reinhard, Jürn Schmelzer, and Gerd Röpke. "Das Kolmogorov—Arnold—Moser—Theorem (KAM-Theorem) und einige Konsequenzen." In Nichtlineare Phänomene und Selbstorganisation. Vieweg+Teubner Verlag, 1992. http://dx.doi.org/10.1007/978-3-322-94778-9_6.

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Weissert, Thomas P. "The Kolmogorov-Arnold-Moser Theorem: “Here Comes the Surprise”." In The Genesis of Simulation in Dynamics. Springer New York, 1997. http://dx.doi.org/10.1007/978-1-4612-1956-9_4.

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Feldmeier, Achim. "Proof of the KAM Theorem." In Introduction to Arnold's Proof of the Kolmogorov–Arnold–Moser Theorem. CRC Press, 2022. http://dx.doi.org/10.1201/9781003287803-4.

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Feldmeier, Achim. "Outline of the KAM Proof." In Introduction to Arnold's Proof of the Kolmogorov–Arnold–Moser Theorem. CRC Press, 2022. http://dx.doi.org/10.1201/9781003287803-3.

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Feldmeier, Achim. "Arithmetic Lemmas." In Introduction to Arnold's Proof of the Kolmogorov–Arnold–Moser Theorem. CRC Press, 2022. http://dx.doi.org/10.1201/9781003287803-8.

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Feldmeier, Achim. "Analytic Lemmas." In Introduction to Arnold's Proof of the Kolmogorov–Arnold–Moser Theorem. CRC Press, 2022. http://dx.doi.org/10.1201/9781003287803-5.

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Feldmeier, Achim. "Convergence Lemmas." In Introduction to Arnold's Proof of the Kolmogorov–Arnold–Moser Theorem. CRC Press, 2022. http://dx.doi.org/10.1201/9781003287803-7.

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Feldmeier, Achim. "Geometric Lemmas." In Introduction to Arnold's Proof of the Kolmogorov–Arnold–Moser Theorem. CRC Press, 2022. http://dx.doi.org/10.1201/9781003287803-6.

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Feldmeier, Achim. "Preliminaries." In Introduction to Arnold's Proof of the Kolmogorov–Arnold–Moser Theorem. CRC Press, 2022. http://dx.doi.org/10.1201/9781003287803-2.

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Feldmeier, Achim. "Hamilton Theory." In Introduction to Arnold's Proof of the Kolmogorov–Arnold–Moser Theorem. CRC Press, 2022. http://dx.doi.org/10.1201/9781003287803-1.

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Conference papers on the topic "Kolmogorov-Arnold-Moser Theorem"

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Ni, Song. "RESPONSE SOLUTIONS OF 2-DIMENSIONAL ELLIPTIC DEGENERATE QUASI-PERIODIC SYSTEMS WITH SMALL PARAMETERS." In Pure & Applied Sciences International Conference, 14-15 March 2024, Singapore. Global Research & Development Services, 2024. http://dx.doi.org/10.20319/icstr.2024.19.

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This paper concerns quasi-periodic perturbations with parameters of 2-dimensional degenerate systems. If the equilibrium point of the unperturbed system is elliptic-type degenerate. Assume that the perturbation is real analytic quasi-periodic with diophantine frequency. Without imposing any assumption on the perturbation, we can use a path of equilibrium points to tackle with the Melnikov non-resonance condition, then by the Leray-Schauder Continuation Theorem and the Kolmogorov-Arnold-Moser technique, it is proved that the equation has a small response solution for many sufficiently small para
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Osborne, Alfred R. "Theory of Nonlinear Fourier Analysis: The Construction of Quasiperiodic Fourier Series for Nonlinear Wave Motion." In ASME 2020 39th International Conference on Ocean, Offshore and Arctic Engineering. American Society of Mechanical Engineers, 2020. http://dx.doi.org/10.1115/omae2020-18850.

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Abstract I give a description of nonlinear water wave dynamics using a recently discovered tool of mathematical physics I call nonlinear Fourier analysis (NLFA). This method is based upon and is an application of a theorem due to Baker [1897, 1907] and Mumford [1984] in the field of algebraic geometry and from additional sources by the author [Osborne, 2010, 2018, 2019]. The theory begins with the Kadomtsev-Petviashvili (KP) equation, a two dimensional generalization of the Korteweg-deVries (KdV) equation: Here the NLFA method is derived from the complete integrability of the equation by finit
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Magnitskii, N. A. "The New Approach to Analysis of Hamiltonian Systems." In ASME 2008 International Mechanical Engineering Congress and Exposition. ASMEDC, 2008. http://dx.doi.org/10.1115/imece2008-66609.

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It is shown in the present paper, on the basis of numerical simulations, that in some Hamiltonian systems with two degrees of freedom the transition to chaos takes place not through the destruction of two-dimensional tori of the unperturbed system in accordance with the Kolmogorov-Arnold-Moser (KAM) theory but, on the contrary, through the generation of complicated two-dimensional tori around cycles of the approximating expanded nonlinear dissipative system and through an infinite cascades of bifurcations of generation of new cycles and singular trajectories in accordance with the universal Fe
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