Probability of Occurrence of Some Planar Random Quasi-homogeneous Vector Fields

Abstract The objective of this work is the study probability occurrence phase portraits in a family planar quasi-homogeneous vector fields quasi degree q , that natural extension linear fields, which correspond to $$q=1.$$ q = 1 . We obtain exact values corresponding probabilities terms simple one-variable definite integral only depends on . This explicitly computable case, recovering known results, and it can be expressed either complete elliptic integrals or generalized hypergeometric functions non-linear one. Moreover, appears remarkable phenomenon when even: have center positive, contrast with what happens also odd, where zero.