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# The discriminant set and bifurcation diagram of the integrable case of M. Adler and P. van Moerbeke

2016, Vol. 12, No. 4, pp.  633–650

Author(s): Ryabov P. E., Biryucheva E.

The paper presents explicitly the spectral curve and the discriminant set of the integrable case of M. Adler and P. van Moerbeke. For critical points of rank 0 and 1 of the momentum map we explicitly calculate the characteristic values defining their type. An algorithm is proposed for finding the bifurcation diagram from the real part of the discriminant set with the help of critical points of rank 0 and 1. The algorithm works under the condition that the real part of the discriminant set contains the bifurcation diagram.
Keywords: integrable Hamiltonian systems, spectral curve, discriminant set, bifurcation diagram
Citation: Ryabov P. E., Biryucheva E., The discriminant set and bifurcation diagram of the integrable case of M. Adler and P. van Moerbeke, Rus. J. Nonlin. Dyn., 2016, Vol. 12, No. 4, pp.  633–650
DOI:10.20537/nd1604007