Complex Riccati Equations

Abstract

In this chapter, we show that depending on the coefficients, the complex Riccati equation has one or another homogeneity domain of the space of several complex variables as its integral manifold. A domain D ⊂ ℂⁿ is called a homogeneity domain if there exists an infinite group of analytic automorphisms of this domain onto itself. Homogeneity domains (Cartan—Siegel domains) often occur in many important branches of calculus (for example, in analytic number theory, automorphic function theory, etc. [16, 50, 82, 99]). We present the main facts related to the homogeneity domains.