TY  - GEN
A1  - Reich, Sebastian
T1  - On the local qualitative behavior of differential-algebraic equations
N2  - A theoretical famework for the investigation of the qualitative behavior of differential-algebraic equations (DAEs) near an equilibrium point is established. The key notion of our approach is the notion of regularity. A DAE is called regular locally around an equilibrium point if there is a unique vector field such that the solutions of the DAE and the vector field are in one-to-one correspondence in a neighborhood of this equili Drium point. Sufficient conditions for the regularity of an equilibrium point are stated. This in turn allows us to translate several local results, as formulated for vector fields, to DAEs that are regular locally around a g: ven equilibrium point (e.g. Local Stable and Unstable Manifold Theorem, Hopf theorem). It is important that ihese theorems are stated in terms of the given problem and not in terms of the corresponding vector field.
T3  - Zweitveröffentlichungen der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe - paper 159 
Y1  - 2010
UR  - https://publishup.uni-potsdam.de/frontdoor/index/index/docId/4480
UR  - https://nbn-resolving.org/urn:nbn:de:kobv:517-opus-46739
ER  -