Unique resonant normal forms for area preserving maps at an elliptic fixed point TeX Export

@article{citeulike:3211255, abstract = {We construct a resonant normal form for an area-preserving map near a generic resonant elliptic fixed point. The normal form is obtained by a simplification of a formal interpolating Hamiltonian. The resonant normal form is unique and therefore provides the formal local classification for area-preserving maps with the elliptic fixed point. The total number of formal invariants is infinite. We consider the cases of weak (of order \$n\ge5\$) and strong (of order \$n=3,4\$) resonances. We also construct unique normal forms for analytic families of area-preserving maps. We note that our constructions involve non-linear grading functions.}, archivePrefix = {arXiv}, author = {Gelfreich, V. and Gelfreikh, N.}, citeulike-article-id = {3211255}, citeulike-linkout-0 = {http://arxiv.org/abs/0809.1614}, citeulike-linkout-1 = {http://arxiv.org/pdf/0809.1614}, day = {9}, eprint = {0809.1614}, keywords = {divergence, normal\_forms, singularity}, month = {Sep}, posted-at = {2008-09-10 08:15:27}, priority = {2}, title = {Unique resonant normal forms for area preserving maps at an elliptic fixed point}, url = {http://arxiv.org/abs/0809.1614}, year = {2008} }

TY - JOUR ID - citeulike:3211255 L3 - citeulike-article-id:3211255 N2 - We construct a resonant normal form for an area-preserving map near a generic resonant elliptic fixed point. The normal form is obtained by a simplification of a formal interpolating Hamiltonian. The resonant normal form is unique and therefore provides the formal local classification for area-preserving maps with the elliptic fixed point. The total number of formal invariants is infinite. We consider the cases of weak (of order $n\ge5$) and strong (of order $n=3,4$) resonances. We also construct unique normal forms for analytic families of area-preserving maps. We note that our constructions involve non-linear grading functions. TI - Unique resonant normal forms for area preserving maps at an elliptic fixed point KW - divergence KW - normal_forms KW - singularity AU - Gelfreich, V AU - Gelfreikh, N PY - 2008/Sep/09/ UR - http://arxiv.org/abs/0809.1614 ER -