On the non-smoothness of the vector fields for the dynamically invariant Beltrami coefficients

摘要

For , the vector fields on the unit circle determined by play an important role in the theory of the universal Teichmuller space. The aim of this paper is to give some characterizations of the vector fields induced by dynamically invariant . We show that those vector fields are not contained in the Sobolev class . At last, we give some results on dynamically invariant vectors to show that the vector fields, the quasi-symmetric homeomorphisms, and the quasi-circles are closely related.