On the Diffusion Mechanism in Hamiltonian Systems

IF 0.6 4区 数学 Q3 MATHEMATICS Functional Analysis and Its Applications Pub Date : 2025-01-20 DOI:10.1134/S0016266324040026
Valery Kozlov
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引用次数: 0

Abstract

The diffusion mechanism in Hamiltonian systems, close to completely integrable, is usually connected with the existence of the so-called “transition chains”. In this case slow diffusion occurs in a neighborhood of intersecting separatrices of hyperbolic periodic solutions (or, more generally, lower-dimensional invariant tori) of the perturbed system. In this note we discuss another diffusion mechanism that uses destruction of invariant tori of the unperturbed system with an almost resonant set of frequencies. We demonstrate this mechanism on a particular isoenergetically nondegenerate Hamiltonian system with three degrees of freedom. The same phenomenon also occurs for general higher-dimensional Hamiltonian systems. Drift of slow variables is shown using analysis of integrals of quasi-periodic functions of the time variable (possibly unbounded) with zero mean value. In addition, the proof uses the conditions of topological transitivity for cylindrical cascades.

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关于哈密顿系统中的扩散机制
在接近完全可积的哈密顿系统中,扩散机制通常与所谓的“过渡链”的存在有关。在这种情况下,缓慢扩散发生在摄动系统的双曲周期解(或更一般地说,低维不变环面)相交分离的邻域中。在本文中,我们讨论了另一种扩散机制,该机制利用了具有几乎谐振频率集的无扰动系统的不变环面破坏。我们在一个特定的三自由度等能非简并哈密顿系统上证明了这一机制。同样的现象也发生在一般的高维哈密顿系统中。通过分析时间变量(可能无界)的准周期函数的零平均值的积分,说明了慢变量的漂移。此外,还利用圆柱级联的拓扑传递性条件进行了证明。
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来源期刊
CiteScore
0.90
自引率
0.00%
发文量
7
审稿时长
>12 weeks
期刊介绍: Functional Analysis and Its Applications publishes current problems of functional analysis, including representation theory, theory of abstract and functional spaces, theory of operators, spectral theory, theory of operator equations, and the theory of normed rings. The journal also covers the most important applications of functional analysis in mathematics, mechanics, and theoretical physics.
期刊最新文献
Grothendieck’s Theorem on the Precompactness of Subsets of Functional Spaces over Pseudocompact Spaces An Algebraic Version of the Poincare Construction Bounded-Degree Subgroups of the Cremona Group in \(\mathrm{CR}\)-Geometry On the Differential Operators of Odd Order with \(\mathrm{PT}\)-Symmetric Periodic Matrix Coefficients On the Diffusion Mechanism in Hamiltonian Systems
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