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Abstract
At a twofold 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 towards 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 analysed 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 number of rotations made anywhere in the ﬂow diﬀers only by one, and increases incrementally with a single parameter: the angular jump in the ﬂow direction across the switching manifold, at the singularity.
singularity by sliding along, the switching manifold. The case when the number of rotations around the singularity is inﬁnite has been analysed 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 number of rotations made anywhere in the ﬂow diﬀers only by one, and increases incrementally with a single parameter: the angular jump in the ﬂow direction across the switching manifold, at the singularity.
Original language  English 

Pages (fromto)  115 
Number of pages  15 
Journal  SIAM Journal on Applied Dynamical Systems 
Volume  11 
Issue number  4 
DOIs  
Publication status  Published  2012 
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Projects
 1 Finished

When Worlds Collide: the asymptotics of interacting systems (Career Acceleration Fellowship)
1/08/12 → 1/08/16
Project: Research