Colombo, Alessandro

Jeffrey, Mike R.

Physica D Nonlinear Phenomena

English

A discontinuity in a system of ordinary differential equations can create allow that slides along the discontinuity locus. Prior to sliding, the flow may have collapsed onto the discontinuity, making the reverse flow non-unique, as happens when dry-friction causes objects to stick. Alternatively, a flow may slide along the discontinuity before escaping it at some indeterminable time, implying non-uniqueness in forward time. At a two-fold singularity these two behaviours are brought together, so that a single point may have multiple possible futures as well as histories. Two-folds are a generic consequence of discontinuities in three or more dimensions, and play an important role in both local and global dynamics. Despite this, until now nothing was known about two-fold singularities in systems of more than 3 dimensions. Here, the normal form of the two-fold is extended to higher dimensions, where we show that much of its lower dimensional dynamics survives. (C) 2013 Elsevier B.V. All rights reserved.</p

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The two-fold singularity of nonsmooth flows:Leading order dynamics in n-dimensions

COLOMBO, ALESSANDRO

Mike Jeffrey

Archivio istituzionale della ricerca - Politecnico di Milano

The two-fold singularity of nonsmooth flows: Leading order dynamics in n-dimensions

Alessandro Colombo

Mike R. Jeffrey

Crossref

The two-fold singularity of nonsmooth flows: Leading order dynamics in -dimensions

The two-fold singularity of nonsmooth flows:Leading order dynamics in n-dimensions

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Archivio istituzionale della ricerca - Politecnico di Milano

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