Infinitesimal Lyapunov functions for singular flows
Abstract
We present an extension of the notion of infinitesimal Lyapunov function to singular flows, and from this technique we deduce a characterization of partial/sectional hyperbolic sets. In absence of singularities, we can also characterize uniform hyperbolicity. These conditions can be expressed using the space derivative DX of the vector field X together with a field of infinitesimal Lyapunov functions only, and are reduced to checking that a certain symmetric operator is positive definite at the tangent space of every point of the trapping region.
- Publication:
-
arXiv e-prints
- Pub Date:
- January 2012
- DOI:
- 10.48550/arXiv.1201.2550
- arXiv:
- arXiv:1201.2550
- Bibcode:
- 2012arXiv1201.2550A
- Keywords:
-
- Mathematics - Dynamical Systems;
- Mathematics - Classical Analysis and ODEs;
- 37D30;
- 37D25
- E-Print:
- 37 pages, 1 figure