The geometry of planar flows

نویسنده

  • G. E. Prince
چکیده

We study the linear map, AZ(p) : TpE 2 → TpE associated with the linearization of a planar flow with tangent vector field Z. A quadratic form constructed from this map contains information about the expansion of the flow in an arbitrary direction and its eigenvectors represent directions of maximum and minimum expansion. A second quadratic form provides information about the rotation of the flow and its eigenvectors represent directions whose rotation is maximum and minimum. These two quadratic forms allow a manifestly geometric analysis of planar flows without requiring their explicit solution.

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تاریخ انتشار 1997