☆ 4.2 Article

The reversible context 2 in KAM theory: the first steps

REGULAR & CHAOTIC DYNAMICS (2011)

期刊

REGULAR & CHAOTIC DYNAMICS

卷 16, 期 1-2, 页码 24-38

出版社

MAIK NAUKA/INTERPERIODICA/SPRINGER

DOI: 10.1134/S1560354710520035

关键词

KAM theory; Moser's modifying terms theorem; reversible systems; reversible contexts; fixed point manifold; invariant torus

类别

Mathematics, Applied Mechanics Physics, Mathematical

资金

Russia Federation [NSh-8462.2010.1]

向作者/读者索取更多资源

Protocol

Reagent

摘要

The reversible context 2 in KAM theory refers to the situation where dim FixG < 1/2 codim T, here FixG is the fixed point manifold of the reversing involution G and T is the invariant torus one deals with. Up to now, this context has been entirely unexplored. We obtain a first result on the persistence of invariant tori in the reversible context 2 (for the particular case where dim Fix G = 0) using J. Moser's modifying terms theorem of 1967.

作者

我是这篇论文的作者

点击您的名字以认领此论文并将其添加到您的个人资料中。

评论

主要评分

4.2

评分不足

次要评分

新颖性

-

重要性

-

科学严谨性

-

评价这篇论文

推荐

Article Mathematics

Iso-manifold KAM persistence

Xuefeng Zhao, Yong Li

Summary: We study the iso-manifold persistence in formulism and show that unperturbed tori can give rise to invariant tori in the perturbed system while maintaining the ratio of certain frequency components. We also consider the iso-manifold Melnikov persistence.

JOURNAL OF DIFFERENTIAL EQUATIONS (2022)

添加到收藏夹

Article Mathematics, Applied

Residues of Destructed Resonance Torus

Chong-Qing Cheng, Min Zhou

Summary: In this paper, a method is proposed to address the complete degeneracy problem in lower dimensional invariant tori surviving from destructed resonant torus. As an application, a different proof of the existence of co-dimension one invariant tori is obtained, with no additional assumptions on the perturbation other than its smallness.

JOURNAL OF DYNAMICS AND DIFFERENTIAL EQUATIONS (2021)

添加到收藏夹

Article Mathematics, Applied

A MOSER'S NON-TWIST THEOREM FOR NEARLY INTEGRABLE MAPPINGS WITH SELF-INTERSECTION PROPERTY

Zhichao Ma, Junxiang Xu

Summary: In this paper, we investigate a family of nearly integrable mappings on an annulus, which have self-intersection property and depend on a small parameter. Despite the absence of a twist condition, we demonstrate that for many sufficiently small parameters, these mappings possess an invariant closed curve. Our findings have implications for the Lagrange stability of Duffing equations.

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY (2023)

添加到收藏夹

Article Mathematics, Applied

KAM THEOREM AND ISO-ENERGETIC KAM THEOREM ON POISSON MANIFOLD

Weichao Qian

Summary: In this paper, the KAM theorem and the iso-energetic KAM theorem are presented for Hamiltonian systems on n-dimensional Poisson manifold (M, pi) with rank of pi equal to 2r everywhere, where pi is a given bivector field and 2r < n.

JOURNAL OF APPLIED ANALYSIS AND COMPUTATION (2023)

添加到收藏夹

Article Mathematics, Applied

KAM THEOREM FOR REVERSIBLE MAPPING OF LOW SMOOTHNESS WITH APPLICATION

Jing Li, Jiangang Qi, Xiaoping Yuan

Summary: Assuming a reversible mapping A with certain conditions, an invariant torus with rotational frequency omega can be found. This result is applicable to proving the Lagrange stability of a reversible Duffing equation with finite smooth perturbation.

DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS (2023)

添加到收藏夹

Article Mathematics

Persistence of multi-dimensional degenerate hyperbolic lower dimensional invariant tori in reversible systems ?

Xiaomei Yang, Junxiang Xu

Summary: In this paper, the persistence of multi-dimensional degenerate hyperbolic lower dimensional invariant tori with prescribed frequencies in reversible systems is proven using KAM techniques and topological degree theory.

JOURNAL OF DIFFERENTIAL EQUATIONS (2023)

添加到收藏夹

Article Mathematics, Applied

Persistence of Degenerate Lower Dimensional Invariant Tori in Reversible Systems with Bruno Non-degeneracy Conditions

Xiaomei Yang, Junxiang Xu

Summary: This paper investigates a class of degenerate reversible systems with Bruno non-degeneracy conditions, and proves the persistence of a lower dimensional invariant torus, whose frequency vector is only a small dilation of the prescribed one.

QUALITATIVE THEORY OF DYNAMICAL SYSTEMS (2021)

添加到收藏夹

Article Mathematics, Applied

Persistence of Degenerate Lower Dimensional Invariant Tori with Prescribed Frequencies in Reversible Systems

Xiaomei Yang, Junxiang Xu, Shunjun Jiang

Summary: This paper considers small perturbations of an integrable reversible system with a degenerated lower dimensional invariant torus. By employing KAM technique and stability theory, the persistence of the degenerate lower dimensional invariant torus is proved, without requiring extra conditions on the perturbations except for smallness. This result extends the partial result of Hamiltonian systems to reversible systems, as shown by Xu and You (Regul Chaotic Dyn 25(6):616-650, 2020).

JOURNAL OF DYNAMICS AND DIFFERENTIAL EQUATIONS (2023)

添加到收藏夹

Article Mathematics

Parabolic invariant tori in quasi-periodically forced skew-product maps

Xinyu Guan, Jianguo Si, Wen Si

Summary: This study investigates the existence of parabolic invariant tori for a class of quasi-periodically forced analytic skew-product maps. Different conditions are considered for different scenarios, and it is shown that parabolic invariant tori exist under certain conditions.

JOURNAL OF DIFFERENTIAL EQUATIONS (2021)

添加到收藏夹

Article Mathematics, Applied

Quasi-periodic solutions and homoclinic bifurcation in an impact inverted pendulum

Xiaoming Zhang, Zhenbang Cao, Denghui Li, Celso Grebogi, Jianhua Xie

Summary: We investigate the impact of a nonlinear inverted pendulum between two rigid walls under external periodic excitation. By applying KAM theory, we demonstrate the existence of three regions in phase space (corresponding to different energies) occupied by quasi-periodic solutions when the periodic excitation is small. Furthermore, we observe that the rotational quasi-periodic motion persists as the perturbation increases. The Aubry-Mather theory is utilized to obtain subharmonic periodic solutions, and the boundedness of all solutions is explained by the presence of abundant invariant tori near infinity. Additionally, we propose a numerical method to accurately compute the discontinuous invariant manifolds, which serves as a useful tool for studying invariant manifolds under the effect of impacts.

PHYSICA D-NONLINEAR PHENOMENA (2022)

添加到收藏夹

Article Mathematics, Applied

A KAM Theorem with Large Twist and Finite Smooth Large Perturbation

Lu Chen

Summary: In this study, a class of non-degenerate Hamiltonian systems were investigated. It was proven that under certain conditions, for sufficiently small parameter e, there exists an invariant torus satisfying specific conditions. Additionally, it was found that a finite network of Duffing oscillators with periodic external forces exhibits Lagrange stability for almost all initial data.

QUALITATIVE THEORY OF DYNAMICAL SYSTEMS (2023)

添加到收藏夹

Article Mathematics, Applied

COMPLETELY DEGENERATE LOWER-DIMENSIONAL INVARIANT TORI IN REVERSIBLE SYSTEMS

Tianqi Jing, Wen Si

Summary: This paper investigates the persistence of completely degenerate lower-dimensional invariant tori in a reversible system and proves the existence of such tori under certain conditions using the Kolmogorov-ArnoldMoser method. This is believed to be the first result on the persistence of lower-dimensional invariant tori in completely degenerate reversible systems.

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY (2021)

添加到收藏夹

Article Physics, Mathematical

Quasi-periodic solutions for quintic completely resonant derivative beam equations on T2

Chuanfang Ge, Jiansheng Geng

Summary: In this paper, we investigate two dimensional completely resonant, derivative, quintic nonlinear beam equations with reversible structure. Due to the absence of external parameters or potentials in this reversible system, Birkhoff normal form reduction is necessary before applying Kolmogorov-Arnold-Moser (KAM) theorem. As an application of KAM theorem, the existence of partially hyperbolic, small amplitude, quasi-periodic solutions of the reversible system is proven.

JOURNAL OF MATHEMATICAL PHYSICS (2023)

添加到收藏夹

Article Mathematics, Applied

EXISTENCE OF INVARIANT CURVES FOR DEGENERATE ALMOST PERIODIC REVERSIBLE MAPPINGS

Peng Huang

Summary: This paper investigates the existence of invariant curves for almost periodic reversible mappings with higher order degeneracy of the twist condition. A new variant of the KAM theory, involving an artificial parameter q, 0 < q < 1, is used in the proof to ensure that the steps of the KAM iteration become infinitely small in the speed of function q(n)epsilon, rather than a super exponential function.

DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS (2022)

添加到收藏夹

Article Mathematics

Quasiperiodic Poincaré persistence at high degeneracy

Weichao Qian, Yong Li, Xue Yang

Summary: In this paper, we investigate the persistence of resonant invariant tori in Hamiltonian systems with high-order degenerate perturbation, and prove a quasiperiodic Poincare theorem under high degeneracy, answering a long-standing conjecture on the persistence of resonant invariant tori in general situations.

ADVANCES IN MATHEMATICS (2024)

添加到收藏夹

Article Physics, Atomic, Molecular & Chemical

Statistical characteristics of the motion of a pair of heavy ions in non-convex cavities of complicated geometry with fixed crosspieces and charges

L. I. Kolesnikova, L. Yu. Rusin, M. B. Sevryuk

RUSSIAN JOURNAL OF PHYSICAL CHEMISTRY B (2015)

添加到收藏夹

Article Mathematics, Applied

Whitney smooth families of invariant tori within the reversible context 2 of KAM theory

Mikhail B. Sevryuk

REGULAR & CHAOTIC DYNAMICS (2016)

添加到收藏夹

Article Mathematics, Applied

Families of invariant tori in KAM theory: Interplay of integer characteristics

Mikhail B. Sevryuk

REGULAR & CHAOTIC DYNAMICS (2017)

添加到收藏夹

Article Mathematics, Applied

Statistics of energy partitions for many-particle systems in arbitrary dimension

Vincenzo Aquilanti, Andrea Lombardi, Mikhail B. Sevryuk

REGULAR & CHAOTIC DYNAMICS (2014)

添加到收藏夹

Article Mathematics, Applied

Translation of the V.I. Arnold paper From Superpositions to KAM Theory (Vladimir Igorevich Arnold. Selected-60, Moscow: PHASIS, 1997, pp. 727-740)

Mikhail B. Sevryuk

REGULAR & CHAOTIC DYNAMICS (2014)

添加到收藏夹

Article Physics, Atomic, Molecular & Chemical

Dynamics of a heavy ionic pair in a cavity with an elastic or inelastic boundary, crosspieces, and fixed charges of opposite sign

L. I. Kolesnikova, L. Yu Rusin, M. B. Sevryuk

RUSSIAN JOURNAL OF PHYSICAL CHEMISTRY B (2013)

添加到收藏夹

Article Physics, Atomic, Molecular & Chemical

A Hard Sphere Model for Direct Three-Body Recombination of Heavy Ions

E. V. Ermolova, L. Yu Rusin, M. B. Sevryuk

RUSSIAN JOURNAL OF PHYSICAL CHEMISTRY B (2014)

添加到收藏夹

Article Mathematics

Hamiltonian and reversible systems with smooth families of invariant tori

Mikhail B. Sevryuk

Summary: This paper presents examples of Hamiltonian and reversible systems with smooth d-parameter families of invariant n-tori carrying conditionally periodic motions. The cases of isotropic, coisotropic, and atropic tori in non-compact and compact phase spaces are considered. Additionally, an example of an analytic Hamiltonian system with an isolated invariant N-torus carrying conditionally periodic motions is presented for any N >= 3.

INDAGATIONES MATHEMATICAE-NEW SERIES (2021)

添加到收藏夹

Article Chemistry, Physical

Detailed dynamics of direct three-body recombination of singly charged ions

Vyacheslav M. Akimov, Vladimir M. Azriel', Ekaterina V. Ermolova, Dmitrii B. Kabanov, Lyubov' I. Kolesnikova, Lev Yu. Rusin, Mikhail B. Sevryuk

Summary: This paper investigates the detailed dynamics of direct three-body ion-ion recombination reactions, considering the main aspects of non-central ion encounters. The reactions are simulated using the quasiclassical trajectory method with diabatic semiempirical potential energy surfaces. The recombination mechanisms are studied through visualization of randomly selected trajectories, and a comparison is made between trajectories with identical initial conditions for different systems.

PHYSICAL CHEMISTRY CHEMICAL PHYSICS (2022)

添加到收藏夹

Article Multidisciplinary Sciences

Statistical dynamics of bimolecular recombination of alkali and halide ions

Vyacheslav M. Akimov, Vladimir M. Azriel, Ekaterina V. Ermolova, Dmitrii B. Kabanov, Lev Yu. Rusin, Mikhail B. Sevryuk

Summary: By simulating the dynamics of bimolecular recombination reactions under different conditions, it was found that the collision energy has important effects on the recombination cross section and the energy distribution of products. The type of halide ion also plays a significant role in the dynamics.

RENDICONTI LINCEI-SCIENZE FISICHE E NATURALI (2022)

添加到收藏夹

Article Chemistry, Physical

Dynamics of third order direct three-body recombination of heavy ions

Vyacheslav M. Akimov, Vladimir M. Azriel, Ekaterina Ermolova, Dmitrii B. Kabanov, Lyubov' Kolesnikova, Lev Yu Rusin, Mikhail B. Sevryuk

Summary: The direct three-body recombination reactions Cs+ + X- + R -> CsX + R (X = F, I and R = Ar, Xe) were studied using the quasiclassical trajectory method, revealing the distinct features of different recombination pairs and the superior efficiency of xenon in accepting excess energy from ion pairs. The resulting energy distributions of the recombination products show equilibrium for rotational energy in CsF and CsI molecules, but strong non-equilibrium for vibrational energy.

PHYSICAL CHEMISTRY CHEMICAL PHYSICS (2021)

添加到收藏夹

Article Multidisciplinary Sciences

Scattering of particles from a solid surface: the impulsive model of composite encounters

Vyacheslav M. Akimov, Vladimir M. Azriel, Lyubov I. Kolesnikova, Lev Yu. Rusin, Mikhail B. Sevryuk

RENDICONTI LINCEI-SCIENZE FISICHE E NATURALI (2019)

添加到收藏夹

Article Physics, Atomic, Molecular & Chemical

Two Mechanisms of Recombination of Atomic Ions

V. M. Azriel', V. M. Akimov, E. V. Ermolova, D. B. Kabanov, L. I. Kolesnikova, L. Yu. Rusin, M. B. Sevryuk

RUSSIAN JOURNAL OF PHYSICAL CHEMISTRY B (2018)

添加到收藏夹

Article Physics, Atomic, Molecular & Chemical

Dissociation of Potassium Iodide at a Graphite Surface within the Framework of an Impulsive Model

V. M. Azriel', V. M. Akimov, E. V. Ermolova, L. I. Kolesnikova, L. Yu. Rusin, M. B. Sevryuk

RUSSIAN JOURNAL OF PHYSICAL CHEMISTRY B (2018)

添加到收藏夹

Article Mathematics, Applied

HERMAN'S APPROACH TO QUASI-PERIODIC PERTURBATIONS IN THE REVERSIBLE KAM CONTEXT 2

Mikhail B. Sevryuk

MOSCOW MATHEMATICAL JOURNAL (2017)

添加到收藏夹

暂无数据

© Peeref 2019-2024. All rights reserved.