Sliding motion on the intersection of two manifolds: Spirally attractive case

Abstract

In this note, we consider sliding motion on the intersection Σ of two smooth manifolds in the case when the dynamics near the manifold Σ is spiral-like, and Σ is spirally attractive. We clarify the meaning of spiral-like dynamics around Σ, characterize what we mean by spiral attractivity of Σ, and finally discuss what to expect when Σ ceases to be attractive, with nearby orbits getting farther away from Σ through spiraling motion. Our characterization of spiral-attractivity of Σ is given by a single number, which plays a role similar to that of a Floquet multiplier for a smooth planar system.