The composition conjecture for Abel equation
The paper deals with the composition conjecture for the Abel differential equation \[ \dot{z}=A(t)z^3+B(t)z^2, \] where \(z\) is real and \(A,B\) are continuous functions. It states that if all solutions in a neighborhood of the origin are periodic then the indefinite integrals of coefficients from the equation are compositions of a periodic functions. By means of the Cherkas transformation the author explains the relations with the classical center problem. At present the conjecture is verified for a particular cases, when the coefficients are polynomial functions of small degrees or have small number of terms. Therefore, the author presents a widely accessible exposition of the conjecture and verifies it for certain classes of coefficients.
scientific article; zbMATH DE number 5572050
scientific article