Invariants in Separated Variables: Yang-Baxter, Entwining and Transfer Maps
| Autor: | Pavlos Kassotakis |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2019 |
| Předmět: |
Pure mathematics
Integrable system Nonlinear Sciences - Exactly Solvable and Integrable Systems 010102 general mathematics FOS: Physical sciences 01 natural sciences Transfer (group theory) Nonlinear Sciences::Exactly Solvable and Integrable Systems Mathematics::Quantum Algebra 0103 physical sciences Gravitational singularity 010307 mathematical physics Geometry and Topology Exactly Solvable and Integrable Systems (nlin.SI) 0101 mathematics General position Mathematical Physics Analysis Mathematics |
| Popis: | We present the explicit form of a family of Liouville integrable maps in 3 variables, the so-called triad family of maps and we propose a multi-field generalisation of the latter. We show that by imposing separability of variables to the invariants of this family of maps, the $H_{\rm I}$, $H_{\rm II}$ and $H_{\rm III}^A$ Yang-Baxter maps in general position of singularities emerge. Two different methods to obtain entwining Yang-Baxter maps are also presented. The outcomes of the first method are entwining maps associated with the $H_{\rm I}$, $H_{\rm II}$ and $H_{\rm III}^A$ Yang-Baxter maps, whereas by the second method we obtain non-periodic entwining maps associated with the whole $F$ and $H$-list of quadrirational Yang-Baxter maps. Finally, we show how the transfer maps associated with the $H$-list of Yang-Baxter maps can be considered as the $(k-1)$-iteration of some maps of simpler form. We refer to these maps as extended transfer maps and in turn they lead to $k$-point alternating recurrences which can be considered as alternating versions of some hierarchies of discrete Painlev\'e equations. |
| Databáze: | OpenAIRE |
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