Integrable mappings with transcendental invariants

作者: B. Grammaticos , A. Ramani

DOI: 10.1016/J.CNSNS.2005.03.005

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摘要: Abstract We examine a family of integrable mappings which possess rational invariants involving polynomials arbitrarily high degree. Next we extend these to the case where their parameters are functions independent variable. The resulting do not preserve any invariant but solvable by linearisation. Using this result then proceed construct solution initial autonomous and use it explicitly invariant, turns out be transcendental in generic case.

参考文章(12)
Jarmo Hietarinta, Claude Viallet, SINGULARITY CONFINEMENT AND CHAOS IN DISCRETE SYSTEMS Physical Review Letters. ,vol. 81, pp. 325- 328 ,(1998) , 10.1103/PHYSREVLETT.81.325
A. Ramani, A.S. Carstea, B. Grammaticos, Y. Ohta, On the autonomous limit of discrete Painlevé equations Physica A-statistical Mechanics and Its Applications. ,vol. 305, pp. 437- 444 ,(2002) , 10.1016/S0378-4371(01)00619-7
A Ramani, B Grammaticos, Y Ohta, S Lafortune, Linearizable mappings and the low-growth criterion Journal of Physics A. ,vol. 33, ,(2000) , 10.1088/0305-4470/33/31/104
K Kimura, H Yahagi, R Hirota, A Ramani, B Grammaticos, Y Ohta, A new class of integrable discrete systems Journal of Physics A. ,vol. 35, pp. 9205- 9212 ,(2002) , 10.1088/0305-4470/35/43/315
B. Grammaticos, T. Tamizhmani, A. Ramani, A. S. Carstea, K. M. Tamizhmani, A Bilinear Approach to the Discrete Painlevé I Equations Journal of the Physical Society of Japan. ,vol. 71, pp. 443- 447 ,(2002) , 10.1143/JPSJ.71.443
B. Grammaticos, A. Ramani, V. Papageorgiou, Do integrable mappings have the Painlevé property Physical Review Letters. ,vol. 67, pp. 1825- 1828 ,(1991) , 10.1103/PHYSREVLETT.67.1825
A. Ramani, B. Grammaticos, J. Hietarinta, Discrete versions of the Painlevé equations. Physical Review Letters. ,vol. 67, pp. 1829- 1832 ,(1991) , 10.1103/PHYSREVLETT.67.1829
Y. Ohta, K.M. Tamizhmani, B. Grammaticos, A. Ramani, Singularity confinement and algebraic entropy: the case of the discrete Painlevé equations Physics Letters A. ,vol. 262, pp. 152- 157 ,(1999) , 10.1016/S0375-9601(99)00670-2
Jarmo Hietarinta, Direct methods for the search of the second invariant Physics Reports. ,vol. 147, pp. 87- 154 ,(1987) , 10.1016/0370-1573(87)90089-5