# Vector Fields with a non-degenerate Source

#### Autoren: Matthias Ludewig (2014)

We discuss the solution theory of operators of the form ∇X + A, acting on smooth sections of a vector bundle with connection ∇ over a manifold M, where X is a vector field having a critical point with positive linearization at some point p ∈ M. As an operator on a suitable space of smooth sections Γ(U, V), it fulfills a Fredholm alternative, and the same is true for the adjoint operator. Furthermore, we show that the solutions depend smoothly on the data ∇, X and A.

Zeitschrift:
J. Geom. Phys.
Verlag:
Elsevier
Seiten:
59-76
Band:
79

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