黎曼覆盖上的变量分离与超可积性

IF 0.9 3区 物理与天体物理 Q2 MATHEMATICS Symmetry Integrability and Geometry-Methods and Applications Pub Date : 2022-08-26 DOI:10.3842/SIGMA.2023.062
C. Chanu, G. Rastelli
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引用次数: 0

摘要

我们引入了具有翘曲流形结构的某些常曲率黎曼流形的覆盖流形$M_k$上的Stäckel可分离坐标,其中$k$是有理参数。这些覆盖流形在文献中隐含地表现为与具有任意高阶动量第一积分多项式的超积分系统相连,例如Tremblay-Turbiner-Winternitz系统。我们在这里首次研究了这些流形上自然哈密顿系统的多可分离性和超积分性,并观察了这些性质如何依赖于参数$k$。
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Separation of Variables and Superintegrability on Riemannian Coverings
We introduce Stäckel separable coordinates on the covering manifolds $M_k$, where $k$ is a rational parameter, of certain constant-curvature Riemannian manifolds with the structure of warped manifold. These covering manifolds appear implicitly in literature as connected with superintegrable systems with polynomial in the momenta first integrals of arbitrarily high degree, such as the Tremblay-Turbiner-Winternitz system. We study here for the first time multiseparability and superintegrability of natural Hamiltonian systems on these manifolds and see how these properties depend on the parameter $k$.
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来源期刊
CiteScore
1.80
自引率
0.00%
发文量
87
审稿时长
4-8 weeks
期刊介绍: Scope Geometrical methods in mathematical physics Lie theory and differential equations Classical and quantum integrable systems Algebraic methods in dynamical systems and chaos Exactly and quasi-exactly solvable models Lie groups and algebras, representation theory Orthogonal polynomials and special functions Integrable probability and stochastic processes Quantum algebras, quantum groups and their representations Symplectic, Poisson and noncommutative geometry Algebraic geometry and its applications Quantum field theories and string/gauge theories Statistical physics and condensed matter physics Quantum gravity and cosmology.
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