At a two-fold singularity, the velocity vector of a flow switches discontinuously across a codimension one switching manifold, between two directions that both lie tangent to the manifold. Particularly intricate dynamics arises when the local flow curves toward the switching manifold from both sides, a case referred to as the Teixeira singularity. The flow locally performs two different actions: it winds around the singularity by crossing repeatedly through, and passes through the singularity by sliding along, the switching manifold. The case when the number of rotations around the singularity is infinite has been analyzed in detail. Here we study the case when the flow makes a finite, but previously unknown, number of rotations around the singularity between incidents of sliding. We show that the solution is remarkably simple: the maximum and minimum numbers of rotations made anywhere in the flow differ only by one and increase incrementally with a single parameter---the angular jump in the flow direction across the switching manifold at the singularity.

S. Fernández-García

D. Angulo García

G. Olivar Tost

M. di Bernardo

M. R. Jeffrey

SIAM Journal on Applied Dynamical Systems

SIAM JOURNAL ON APPLIED DYNAMICAL SYSTEMS (SIADS) 发表关于动力系统的数学分析和建模及其在物理、工程、生命和社会科学中的应用的研究文章。 SIADS 仅以电子格式发布。

The SIAM Journal on Applied Dynamical Systems (SIADS) publishes research articles on the mathematical analysis and modeling of dynamical systems and their applications in physics, engineering, life sciences, and social sciences. SIADS is published exclusively in electronic format.

SIAM Journal on Applied Dynamical Systems (SIADS) 发表关于动力系统的数学分析、建模及其在物理、工程、生命科学和社会科学中的应用研究文章。SIADS 仅以电子格式发布。

Structural Stability of the Two-Fold Singularity

This work studies the case when the flow makes a finite, but previously unknown, number of rotations around the singularity between incidents of sliding, and shows that the solution is remarkably simple.

Category	Quartile
数学	4
数学, 物理数学物理	3
数学, 应用数学	4

Structural Stability of the Two-Fold Singularity

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Journal Info

Category	Quartile
PHYSICS, MATHEMATICAL	2