  We present a theoretical framework for understanding the wavefunctions and
spectrum of an extensively studied paradigm for quasiperiodic systems, namely
the Fibonacci chain. Our analytical results, which are obtained in the limit of
strong modulation of the hopping amplitudes, are in good agreement with
published numerical data. In the perturbative limit, we show a new symmetry of
wavefunctions under permutation of site and energy indices. We compute the
wavefunction renormalization factors and from them deduce analytical
expressions for the fractal exponents corresponding to individual
wavefunctions, as well as their global averages. The multifractality of
wavefunctions is seen to appear at next-to-leading order in the ratio of the
hopping amplitudes, $\rho$. Exponents for the local spectral density are given,
in extremely good accord with numerical calculations. Interestingly, our
analytical results for exponents are observed to describe the system rather
well even for values of $\rho$ well outside the domain of applicability of
perturbation theory.
