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

In this note, we consider sliding motion on the intersection Sigma of two smooth manifolds in the case when the dynamics near the manifold Sigma is spiral-like, and Sigma is spirally attractive. We clarify the meaning of spiral-like dynamics around Sigma, characterize what we mean by spiral attractivity of Sigma, and finally discuss what to expect when Sigma ceases to be attractive, with nearby orbits getting farther away from Sigma through spiraling motion. Our characterization of spiral-attractivity of Sigma is given by a single number, which plays a role similar to that of a Floquet multiplier for a smooth planar system. (C) 2015 Elsevier B.V. All rights reserved.