Variational analysis for the multifractal spectra of local entropies and Lyapunov exponents

In a previous article [Chaos, Solitons and Fractals, 13 (2002) 1037], the authors have analyzed the multifractal Lyapunov spectrum. Here we continue that study by considering perturbations of the potential and the dynamics to obtain variational expressions for the entropies and Lyapunov spectra. The spirit and the framework of this note is to obtain, beyond hyperbolicity, variational results, some of which are new and some other which have already been derived but under stronger conditions.