Quaternionic-valued ordinary differential equations. II: Coinciding sectors (Q763752)

This interesting paper is a continuation of two papers by the author [ibid. 246, No. 7, 2762--2787 (2009; Zbl 1170.34028); ibid. 247, No. 7, 2163--2187 (2009; Zbl 1191.34054)]. Using Wazewski's method and Brouwer's fixed point theorem, the author extends to the case of quaternionic-valued ordinary differential equations with polynomial right-hand side some of the existence results he has obtained for the complex-valued case. His approach also leads to uniqueness conditions and to solutions which are heteroclinic to the periodic ones. Some geometric sets, called sectors, provide a localization of the periodic solutions.