广义双括号向量场

IF 1.1 3区数学 Q3 MATHEMATICS, APPLIED

Mathematical Physics, Analysis and Geometry Pub Date : 2025-09-15 DOI:10.1007/s11040-025-09527-x

Petre Birtea, Zohreh Ravanpak, Cornelia Vizman

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引用次数: 0

摘要

利用对称逆变2张量场，将双括号向量场推广到具有伪黎曼度规的泊松流形。我们在紧半简单李代数的伴随轨道上扩展了法度量，以保证这些向量场在每一个辛叶上成为梯度向量场。此外，我们应用这个构造来增强哈密顿系统的平衡点，特别是通过从广义双括号向量场导出的耗散项来解决已经稳定的渐近稳定点的挑战。

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Generalized Double Bracket Vector Fields

We generalize double bracket vector fields, originally defined on semisimple Lie algebras, to Poisson manifolds equipped with a pseudo-Riemannian metric by utilizing a symmetric contravariant 2-tensor field. We extend the normal metric on an adjoint orbit of a compact semisimple Lie algebra to ensure that these vector fields become gradient vector fields on each symplectic leaf. Furthermore, we apply this construction to enhance the equilibria of Hamiltonian systems, specifically addressing the challenge of asymptotically stabilizing points that are already stable, through dissipation terms derived from generalized double bracket vector fields.

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来源期刊

Mathematical Physics, Analysis and Geometry 数学-物理：数学物理

CiteScore

2.10

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： MPAG is a peer-reviewed journal organized in sections. Each section is editorially independent and provides a high forum for research articles in the respective areas. The entire editorial board commits itself to combine the requirements of an accurate and fast refereeing process. The section on Probability and Statistical Physics focuses on probabilistic models and spatial stochastic processes arising in statistical physics. Examples include: interacting particle systems, non-equilibrium statistical mechanics, integrable probability, random graphs and percolation, critical phenomena and conformal theories. Applications of probability theory and statistical physics to other areas of mathematics, such as analysis (stochastic pde''s), random geometry, combinatorial aspects are also addressed. The section on Quantum Theory publishes research papers on developments in geometry, probability and analysis that are relevant to quantum theory. Topics that are covered in this section include: classical and algebraic quantum field theories, deformation and geometric quantisation, index theory, Lie algebras and Hopf algebras, non-commutative geometry, spectral theory for quantum systems, disordered quantum systems (Anderson localization, quantum diffusion), many-body quantum physics with applications to condensed matter theory, partial differential equations emerging from quantum theory, quantum lattice systems, topological phases of matter, equilibrium and non-equilibrium quantum statistical mechanics, multiscale analysis, rigorous renormalisation group.