Year: 2017
Type: preprint
Abstract: In recent work it was shown how recursive factorisation of certain QRT maps leads to Somos-4 and Somos-5 recurrences with periodic coefficients, and to a fifth-order recurrence with the Laurent property. Here we recursively factorise the 12-parameter symmetric QRT map, given by a second-order recurrence, to obtain a system of three coupled recurrences which possesses the Laurent property. As degenerate special cases, we first derive systems of two coupled recurrences corresponding to the 5-parameter multiplicative and additive symmetric QRT maps. In all cases, the Laurent property is established using a generalisation of a result due to Hickerson, and exact formulae for degree growth are found from ultradiscrete (tropical) analogues of the recurrences. For the general 18-parameter QRT map it is shown that the components of the iterates can be written as a ratio of quantities that satisfy the same Somos-7 recurrence.
Source: arXiv (Cornell University)
Authors: Hamad, K., Hone, A. N. W., van der Kamp, P. H., Quispel, G. R. W.
Institutions: La Trobe University, University of Kent
Language: English
Topic: Nonlinear Waves and Solitons
Subfield: Statistical and Nonlinear Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
Award: G4536800330
OpenAlex ID: W2592148178