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Relevant bibliographies by topics / Nekhoroshev Theorem

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Academic literature on the topic 'Nekhoroshev Theorem'

Author: Grafiati

Published: 9 March 2023

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Journal articles on the topic "Nekhoroshev Theorem"

1

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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2

Bambusi, Dario, and Beatrice Langella. "A $C^\infty$ Nekhoroshev theorem." Mathematics in Engineering 3, no. 2 (2021): 1–17. http://dx.doi.org/10.3934/mine.2021019.

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3

Gaeta, Giuseppe. "The Poincaré–Lyapounov–Nekhoroshev Theorem." Annals of Physics 297, no. 1 (2002): 157–73. http://dx.doi.org/10.1006/aphy.2002.6238.

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4

Guzzo, M. "The nekhoroshev theorem and long-term stabilities in the solar system." Serbian Astronomical Journal, no. 190 (2015): 1–10. http://dx.doi.org/10.2298/saj1590001g.

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The Nekhoroshev theorem has been often indicated in the last decades as the reference theorem for explaining the dynamics of several systems which are stable in the long-term. The Solar System dynamics provides a wide range of possible and useful applications. In fact, despite the complicated models which are used to numerically integrate realistic Solar System dynamics as accurately as possible, when the integrated solutions are chaotic the reliability of the numerical integrations is limited, and a theoretical long-term stability analysis is required. After the first formulation of Nekhorosh

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5

FIORANI, EMANUELE. "GEOMETRICAL ASPECTS OF INTEGRABLE SYSTEMS." International Journal of Geometric Methods in Modern Physics 05, no. 03 (2008): 457–71. http://dx.doi.org/10.1142/s0219887808002886.

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We review some basic theorems on integrability of Hamiltonian systems, namely the Liouville–Arnold theorem on complete integrability, the Nekhoroshev theorem on partial integrability and the Mishchenko–Fomenko theorem on noncommutative integrability, and for each of them we give a version suitable for the noncompact case. We give a possible global version of the previous local results, under certain topological hypotheses on the base space. It turns out that locally affine structures arise naturally in this setting.

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Froeschlé, Claude, and Elena Lega. "On the Diffusion Along Resonant Lines in Continuous and Discrete Dynamical Systems." International Journal of Modern Physics B 17, no. 22n24 (2003): 3964–76. http://dx.doi.org/10.1142/s0217979203023033.

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We detect and measure diffusion along resonances in a discrete symplectic map for different values of the coupling parameter. Qualitatively and quantitatively the results are very similar to those obtained for a quasi-integrable Hamiltonian system, i.e. in agreement with Nekhoroshev predictions, although the discrete mapping does not fulfill completely, a priori, the conditions of the Nekhoroshev theorem.

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Todorovic, N. "The role of a steepness parameter in the exponential stability of a model problem: Numerical aspects." Serbian Astronomical Journal, no. 182 (2011): 25–33. http://dx.doi.org/10.2298/saj1182025t.

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The Nekhoroshev theorem considers quasi integrable Hamiltonians providing stability of actions in exponentially long times. One of the hypothesis required by the theorem is a mathematical condition called steepness. Nekhoroshev conjectured that different steepness properties should imply numerically observable differences in the stability times. After a recent study on this problem (Guzzo et al. 2011, Todorovic et al. 2011) we show some additional numerical results on the change of resonances and the diffusion laws produced by the increasing effect of steepness. The experiments are performed o

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8

Henrici, Andreas. "Nekhoroshev Stability for the Dirichlet Toda Lattice." Symmetry 10, no. 10 (2018): 506. http://dx.doi.org/10.3390/sym10100506.

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In this work, we prove a Nekhoroshev-type stability theorem for the Toda lattice with Dirichlet boundary conditions, i.e., with fixed ends. The Toda lattice is a member of the family of Fermi-Pasta-Ulam (FPU) chains, and in view of the unexpected recurrence phenomena numerically observed in these chains, it has been a long-standing research aim to apply the theory of perturbed integrable systems to these chains, in particular to the Toda lattice which has been shown to be a completely integrable system. The Dirichlet Toda lattice can be treated mathematically by using symmetries of the periodi

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9

Xue, Jinxin. "Continuous averaging proof of the Nekhoroshev theorem." Discrete & Continuous Dynamical Systems - A 35, no. 8 (2015): 3827–55. http://dx.doi.org/10.3934/dcds.2015.35.3827.

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10

Moszynski, M. "A quantum version of the Nekhoroshev theorem." Journal of Physics A: Mathematical and General 25, no. 8 (1992): L443—L448. http://dx.doi.org/10.1088/0305-4470/25/8/011.

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Dissertations / Theses on the topic "Nekhoroshev Theorem"

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Schirinzi, Gabriella. "Investigation of new conditions for steepness from a former result by Nekhoroshev." Doctoral thesis, Università degli studi di Padova, 2014. http://hdl.handle.net/11577/3423527.

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This Thesis presents the construction of new sufficient conditions for the verification of a property of functions called steepness. It is a peculiar property required for the application of the Nekhoroshev Theorem to a quasi-integrable Hamiltonian system, and its formulation is given by Nekhoroshev in an implicit way. Therefore sufficient conditions are necessary for the verification of the steepness. Nekhoroshev formulated his celebrated Theorem in the seventies, providing under suitable hypothesis a strong stability result for those dynamical systems which are not integrable, but can be co

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LANGELLA, BEATRICE. "NORMAL FORM AND KAM METHODS FOR HIGHER DIMENSIONAL LINEAR PDES." Doctoral thesis, Università degli Studi di Milano, 2020. http://hdl.handle.net/2434/798372.

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In this thesis an approach to linear PDEs on higher dimensional spatial domains is proposed. I prove two kinds of results: first I develop an algorithm which enables to obtain reducibility for linear PDEs which depend quasi-periodically on time, and I apply it to a quasilinear transport equation of the form ∂_t u= ν•∇u+ ε P (ωt)u on the d-dimensional torus T^d, where ε is a small parameter, ν and ω are Diophantine vectors, P (ωt)=V(x,ωt)•∇+W(ωt), V is a smooth function on T^(d+n) and W(ωt) is an unbounded pseudo-differential operator of order strictly less than 1. The strategy is an extensi

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3

Fontanari, Daniele. "Quantum manifestations of the adiabatic chaos of perturbed susperintegrable Hamiltonian systems." Thesis, Littoral, 2013. http://www.theses.fr/2013DUNK0356/document.

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Dans cette thèse nous étudions un système quantique, obtenu comme un analogue d'un système classique superintégrable perturbé au moyen de la quantification géométrique. Notre objectif est de mettre en évidence la présence des phénomènes analogues à ceux qui caractérisent la superintégrabilité classique, notamment la coexistence des mouvements réguliers et chaotiques liés aux effets des résonances ainsi que la régularité du régime non-résonant. L'analyse est effectuée par l'étude des distributions du Husimi des états quantiques sélectionnés, avec une attention particulière aux états stationnair

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Books on the topic "Nekhoroshev Theorem"

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Giancarlo, Benettin, Henrard J, Kuksin Sergej B. 1955-, Giorgilli Antonio, Centro internazionale matematico estivo, and European Mathematical Society, eds. Hamiltonian dynamics theory and applications: Lectures given at the C.I.M.E.-E.M.S. Summer School, held in Cetraro, Italy, July 1-10, 1999. Springer, 2005.

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2

Henrard, Jacques, Giancarlo Benettin, and Sergei Kuksin. Hamiltonian Dynamics - Theory and Applications: Lectures given at the C.I.M.E. Summer School held in Cetraro, Italy, July 1-10, 1999 (Lecture Notes in Mathematics / Fondazione C.I.M.E., Firenze). Springer, 2005.

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3

Benettin, Giancarlo, Jacques Henrard, Sergej B. Kuksin, and Antonio Giorgilli. Hamiltonian Dynamics - Theory and Applications: Lectures Given at the C. I. M. E. Summer School Held in Cetraro, Italy, July 1-10 1999. Springer London, Limited, 2010.

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Book chapters on the topic "Nekhoroshev Theorem"

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Benettin, Giancarlo. "Physical Applications of Nekhoroshev Theorem and Exponential Estimates." In Lecture Notes in Mathematics. Springer Berlin Heidelberg, 2005. http://dx.doi.org/10.1007/978-3-540-31541-4_1.

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2

Morbidelli, Alessandro, and Massimiliano Guzzo. "The Nekhoroshev Theorem and the Asteroid Belt Dynamical System." In The Dynamical Behaviour of our Planetary System. Springer Netherlands, 1997. http://dx.doi.org/10.1007/978-94-011-5510-6_8.

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3

Guzzo, Massimiliano. "Long-Term Stability Analysis of Quasi Integrable Degenerate Systems through the Spectral Formulation of the Nekhoroshev Theorem." In Modern Celestial Mechanics: From Theory to Applications. Springer Netherlands, 2002. http://dx.doi.org/10.1007/978-94-017-2304-6_19.

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4

Niederman, Laurent. "Nekhoroshev Theory." In Perturbation Theory. Springer US, 2009. http://dx.doi.org/10.1007/978-1-0716-2621-4_352.

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Guzzo, Massimiliano, Zoran Knežević, and Andrea Milani. "Probing the Nekhoroshev Stability of Asteroids." In Modern Celestial Mechanics: From Theory to Applications. Springer Netherlands, 2002. http://dx.doi.org/10.1007/978-94-017-2304-6_8.

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6

Delshams, Amadeu, and Pere Gutiérrez. "Nekhoroshev and KAM Theorems Revisited via a Unified Approach." In Hamiltonian Mechanics. Springer US, 1994. http://dx.doi.org/10.1007/978-1-4899-0964-0_29.

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7

Fortunati, Alessandro, and Stephen Wiggins. "The Kolmogorov-Arnold-Moser (KAM) and Nekhoroshev Theorems with Arbitrary Time Dependence." In Essays in Mathematics and its Applications. Springer International Publishing, 2016. http://dx.doi.org/10.1007/978-3-319-31338-2_5.

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8

Morbidelli, A. "Bounds on Diffusion in Phase Space: Connection Between Nekhoroshev and Kam Theorems and Superexponential Stability of Invariant Tori." In Hamiltonian Systems with Three or More Degrees of Freedom. Springer Netherlands, 1999. http://dx.doi.org/10.1007/978-94-011-4673-9_68.

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