A characterization of the Kadomtsev-Petviashvili hierarchy type C (CKP) in terms KP tau-function is given. Namely, we prove that CKP can be identified with restriction odd times flows on locus turning points second flow. The notion clarified and connected tau function. Algebraic-geometrical solutions particular elliptic are discussed detail. new identity for theta-functions curves holomorphic i...

Abstract In this paper we initiate the study of Chebyshev property Abelian integrals generated by a non-generic turning point in planar slow-fast systems. Such generalize produced Hopf (or generic point), introduced Dumortier et al. (Discrete Contin Dyn Syst Ser S 2(4):723–781, 2009), and play an important role studying number limit cycles born from point.