Transformation invariance of Lyapunov exponents

Lyapunov exponents represent important quantities to characterize the properties of dynamical systems. We show that the Lyapunov exponents of two different dynamical systems that can be converted to each other by a transformation of variables are identical. Moreover, we derive sufficient conditions on the transformation for this invariance property to hold. In particular, it turns out that the transformation need not necessarily be globally invertible.