Block-Separation of Variables: a Form of Partial Separation for Natural Hamiltonians

Symmetry Integrability and Geometry-Methods and Applications

article

Claudia Maria Chanu¹  Giovanni Rastelli¹ 

[1] Dipartimento di Matematica, Università di Torino

关键词: Kashaev equation;    hexahedron recurrence;    principal minors of symmetric matrices;    cubical complexes;    s-holomorphicity;    cluster algebras;   

DOI  :  10.3842/SIGMA.2019.013

来源: National Academy of Science of Ukraine

【 摘 要 】

We study twisted products $H=\alpha^rH_r$ of natural autonomous Hamiltonians $H_r$, each one depending on a separate set, called here separate $r$-block, of variables. We show that, when the twist functions $\alpha^r$ are a row of the inverse of a block-Stäckel matrix, the dynamics of $H$ reduces to the dynamics of the $H_r$, modified by a scalar potential depending only on variables of the corresponding $r$-block. It is a kind of partial separation of variables. We characterize this block-separation in an invariant way by writing in block-form classical results of Stäckel separation of variables. We classify the block-separable coordinates of $\mathbb E^3$.

【 授权许可】

Unknown