Projects per year

### Abstract

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.

Original language | English |
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Pages (from-to) | 1215-1230 |

Number of pages | 16 |

Journal | SIAM Journal on Applied Dynamical Systems |

Volume | 11 |

Issue number | 4 |

DOIs | |

Publication status | Published - 2012 |

## Fingerprint Dive into the research topics of 'Structural stability of the two-fold singularity'. Together they form a unique fingerprint.

## Projects

- 1 Finished

### CA Fellowship for Mike Jeffrey - When Worlds Collide: The Asymptotics of Interacting Systems

Jeffrey, M.

Engineering and Physical Sciences Research Council

1/08/11 → 31/07/12

Project: Research council

## Cite this

Fernández-García, S., García, D. A., Tost, G. O., Di Bernardo, M., & Jeffrey, M. R. (2012). Structural stability of the two-fold singularity.

*SIAM Journal on Applied Dynamical Systems*,*11*(4), 1215-1230. https://doi.org/10.1137/120869134