Tropical spectral curves and integrable cellular automata Export

@misc{citeulike:1243268, abstract = {We propose a method to study the integrable cellular automata with periodic boundary conditions, via the tropical spectral curve and its Jacobian. We introduce the tropical version of eigenvector map from the isolevel set to a divisor class on the tropical hyperelliptic curve. We also provide some conjectures related to the divisor class and the Jacobian. Finally, we apply our method to the periodic box and ball system and clarify the algebro-geometrical meaning of the real torus introduced for its initial value problem.}, archivePrefix = {arXiv}, author = {Inoue, Rei and Takenawa, Tomoyuki}, citeulike-article-id = {1243268}, citeulike-linkout-0 = {http://arxiv.org/abs/0704.2471}, citeulike-linkout-1 = {http://arxiv.org/pdf/0704.2471}, day = {19}, eprint = {0704.2471}, keywords = {cellular-automaton, tropical}, month = {Apr}, posted-at = {2007-04-22 08:21:30}, priority = {2}, title = {Tropical spectral curves and integrable cellular automata}, url = {http://arxiv.org/abs/0704.2471}, year = {2007} }

TY - ELEC ID - citeulike:1243268 L3 - citeulike-article-id:1243268 N2 - We propose a method to study the integrable cellular automata with periodic boundary conditions, via the tropical spectral curve and its Jacobian. We introduce the tropical version of eigenvector map from the isolevel set to a divisor class on the tropical hyperelliptic curve. We also provide some conjectures related to the divisor class and the Jacobian. Finally, we apply our method to the periodic box and ball system and clarify the algebro-geometrical meaning of the real torus introduced for its initial value problem. TI - Tropical spectral curves and integrable cellular automata KW - cellular-automaton KW - tropical AU - Inoue, Rei AU - Takenawa, Tomoyuki PY - 2007/Apr/19/ UR - http://arxiv.org/abs/0704.2471 ER -