Abstract In this work we consider the class of partially integrable 3-dimensional piecewise smooth vector fields Y= (X^+, X^-) Y = (X +, X -) with separation set =\ (x, y, z) { {R}³: z=0\} Σ = (x, y, z) ∈ R 3: z = 0 and first integral H (x, y, z) =x²+y²+z² H (x, y, z) = x 2 + y 2 + z 2 that leaves invariant any sphere centered at the origin, {S}_ ²=\ (x, y, z) { {R}³: x²+y²+z²= ²\} S ρ 2 = (x, y, z) ∈ R 3: x 2 + y 2 + z 2 = ρ 2. We denote this class by X X and by Xₙ X n when X^ X ± are polynomial vector fields of degree n. Our main goal is to study piecewise smooth vector fields in the class X₁ X 1 presenting three periodic annuli on the invariant sphere {S}₁² S 1 2 </mml: msubsup
Oliveira et al. (Wed,) studied this question.