The structure on invariant measures of C 1 generic diffeomorphisms

Let . be an isolated non-trivial transitive set of a C 1 generic diffeomorphism f . Diff(M). We show that the space of invariant measures supported on . coincides with the space of accumulation measures of time averages on one orbit. Moreover, the set of points having this property is residual in . (which implies that the set of irregular+ points is also residual in .). As an application, we show that the non-uniform hyperbolicity of irregular+ points in . with totally 0 measure (resp., the non-uniform hyperbolicity of a generic subset in .) determines the uniform hyperbolicity of ..