Regularization of Brouwer Translation Theorem.

The celebrated Brouwer translation theorem asserts that for a preserving orientation fixed point free homeomorphism of the plane, each point belongs to an invariant region where the dynamics is continuously conjugate to a translation. In this work we prove that if we start with a C m , m ∈ N ∪ { ∞ } , diffeomorphism then the referred conjugacy has the same kind of regularity. [ABSTRACT FROM AUTHOR]