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arXiv · 1703.10785

Covariant geometric characterization of slow invariant manifolds: New concepts and viewpoints

Dirk Lebiedz
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Abstract

We point out a new view on slow invariant manifolds (SIM) in dynamical systems which departs from a purely geometric covariant characterization implying coordinate independency. The fundamental idea is to treat the SIM as a well-defined geometric object in phase space and elucidate characterizing geometric properties that can be evaluated as point-wise analytic criteria. For that purpose, we exploit curvature concepts and formulate our recent variational approach in terms of coordinate-independent Hamiltonian mechanics.Finally, we combine both approaches and conjecture a differential geometric definition of slow invariant manifolds. For the Davis-Skodje model the latter can be completely expatiated.

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Dirk Lebiedz. 2017-03-31. Covariant geometric characterization of slow invariant manifolds: New concepts and viewpoints. https://arxiv.org/abs/1703.10785

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