The redemption of singularity confinement

作者: A Ramani , B Grammaticos , R Willox , T Mase , M Kanki

DOI: 10.1088/1751-8113/48/11/11FT02

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摘要: We present a novel way to apply the singularity confinement property as discrete integrability criterion. shall use what we call full deautonomisation approach, which consists in treating free parameters mapping functions of independent variable, applied complemented with terms that are absent original but do not change structure. show, on host examples including well-known Hietarinta-Viallet, our approach offers compute algebraic entropy for these mappings exactly, thereby allowing one distinguish between integrable and non-integrable cases even when both have confined singularities.

参考文章(10)
Ralph Willox, Takafumi Mase, Alfred Ramani, Basil Grammaticos, Deautonomisation by singularity confinement: an algebro-geometric justification arXiv: Exactly Solvable and Integrable Systems. ,(2014) , 10.1098/RSPA.2014.0956
Teruhisa Tsuda, Basil Grammaticos, Alfred Ramani, Tomoyuki Takenawa, A Class of Integrable and Nonintegrable Mappings and their Dynamics Letters in Mathematical Physics. ,vol. 82, pp. 39- 49 ,(2007) , 10.1007/S11005-007-0200-0
M J Ablowitz, R Halburd, B Herbst, On the extension of the Painlevé property to difference equations Nonlinearity. ,vol. 13, pp. 889- 905 ,(2000) , 10.1088/0951-7715/13/3/321
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
N. Mimura, S. Isojima, M. Murata, J. Satsuma, A. Ramani, B. Grammaticos, Do ultradiscrete systems with parity variables satisfy the singularity confinement criterion Journal of Mathematical Physics. ,vol. 53, pp. 023510- 023510 ,(2012) , 10.1063/1.3682229
Tomoyuki Takenawa, Algebraic entropy and the space of initial values for discrete dynamical systems Journal of Physics A. ,vol. 34, pp. 10533- 10545 ,(2001) , 10.1088/0305-4470/34/48/317
Jarmo Hietarinta, Claude Viallet, Discrete Painlevé I and singularity confinement in projective space Chaos Solitons & Fractals. ,vol. 11, pp. 29- 32 ,(2000) , 10.1016/S0960-0779(98)00266-5
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
Tomoyuki Takenawa, Algebraic entropy and the space of initial values for discrete dynamical systems arXiv: Exactly Solvable and Integrable Systems. ,(2001) , 10.1088/0305-4470/34/48/317