Elliptic functions and their applications in complex differential equations

Abstract: This talk focuses on the applications of elliptic functions in complex differential equations. First, we discuss classifications of meromorphic solutions of certain autonomous complex differential equations. In particular, we will focus on the Loewy factorizable algebraic ODEs. Then we move to the study of the autonomous Schwarzian differential equations (SDEs). Ishizaki showed that there are six canonical types of autonomous SDEs that have transcendental meromorphic solutions. We will construct all transcendental meromorphic solutions of five canonical types explicitly. In particular, the solutions of four types are shown to be elliptic functions. Also, all transcendental meromorphic solutions that possess a Picard exceptional value are characterized for the remaining canonical type. This talk is based on joint works with Ng and Liao respectively.

complex variablesdynamical systems

Audience: researchers in the topic

CAvid: Complex Analysis video seminar

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