Periodic Solutions of Some Polynomial Differential Systems in Dimension 3 via Averaging Theory

Abstract EN

We provide sufficient conditions for the existence of periodic solutions of the polynomial third order differential system x .

= - y + ε P ( x , y , z ) + h 1 ( t ) , y .

= x + ε Q ( x , y , z ) + h 2 ( t ) , and z .

= a z + ε R ( x , y , z ) + h 3 ( t ) , where P , Q , and R are polynomials in the variables x , y , and z of degree n , h i ( t ) = h i ( t + 2 π ) with i = 1,2 , 3 being periodic functions, a is a real number, and ε is a small parameter.