具有一致相对尺寸的流盒定理

A Flowbox Theorem with Uniform Relative Bound

该文讨论了Banach空间中Lipschitz向量场的流盒定理,证明了:若X是一个以L为Lipschitz常数的李氏向量场,则存在与L相关的一个一致常数r_0,使得对X的任意常点x处,存在一个大小为r_0‖X(x)‖的流盒,相应的流盒映射的李氏同胚的Lipschitz常数大小也有一致的控制.

In this paper,we give a flowbox theorem for the Lipschitz vector fields on a Banach spcace.We prove:if X is a Lipschitz vector field with a Lipschitz constant L,then there is a constant r0 associated to L only such that for any regular point x of X,there is a flowbox with size r0||X(x)||,and the Lipschitz constants of the respected lipeomorphism in the flowbox theorem has a uniform bound.