Ohsawa, Tomoki2020-03-242020-03-242019-061941-4889http://dx.doi.org/10.3934/jgm.2019012https://hdl.handle.net/10735.1/7474Due to copyright restrictions and/or publisher's policy full text access from Treasures at UT Dallas is not available. UTD affiliates may be able to acquire a copy through Interlibrary Loan by using the link to UTD ILL.We present an account of dual pairs and the Kummer shapes for n : m resonances that provides an alternative to Holm and Vizman’s work. The advantages of our point of view are that the associated Poisson structure on su(2)* is the standard (+)-Lie–Poisson bracket independent of the values of (n, m) as well as that the Kummer shape is regularized to become a sphere without any pinches regardless of the values of (n, m). A similar result holds for n : −m resonance with a paraboloid and su(1, 1)* . The result also has a straightforward generalization to multidimensional resonances as well. ©2019 American Institute of Mathematical Sciencesen©2019 American Institute of Mathematical SciencesResonanceKummer surfacesarticleOhsawa, T.. 2019. "Dual pairs and regularization of kummer shapes in resonances." Journal of Geometric Mechanics 11(2): 225-238, doi: 10.3934/jgm.2019012112