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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6510 • Differentiable Manifolds

Fall 2015 • Question 3

Question

Math 6510 • Differentiable Manifolds Fall 2015 • Question 3

Let \(V\) be a smooth vector field on \(\mathbb {R}^2\) and assume that outside of a compact set \(V=\frac {\partial }{\partial x}\). Show that the flow for \(V\) is defined for all time.

Raw LaTeX

Let \(V\) be a smooth vector field on \(\R^2\) and assume that outside of a
compact set \(V=\frac{\partial}{\partial x}\). Show that the flow for \(V\) is defined
for all time.

Topic Tags

Left-Invariant Vector Fields Vector Fields and Flows