On bifurcations of cusps

Abstract

Let 𝐹_𝑡, where 𝑡 ∈ ℝ, be an analytic family of plane-to-plane mappings with 𝐹₀ having a critical point at the origin. The paper presents effective algebraic methods of computing the number of those cusp points of 𝐹_𝑡, where 0 < |𝑡| ≪ 1, emanating from the origin at which 𝐹_𝑡 has a positive/negative local topological degree.