Damanik, DavidGorodetski, Anton2013-09-132013-09-132012Damanik, David and Gorodetski, Anton. "The Density of States Measure of the Weakly Coupled Fibonacci Hamiltonian." <i>Geometric and Functional Analysis,</i> 22, (2012) Springer: 976-989. http://dx.doi.org/10.1007/s00039-012-0173-8.https://hdl.handle.net/1911/71898We consider the density of states measure of the Fibonacci Hamiltonian and show that, for small values of the coupling constant V , this measure is exact-dimensional and the almost everywhere value dV of the local scaling exponent is a smooth function of V , is strictly smaller than the Hausdor dimension of the spectrum, and converges to one as V tends to zero. The proof relies on a new connection between the density of states measure of the Fibonacci Hamiltonian and the measure of maximal entropy for the Fibonacci trace map on the non-wandering set in the V -dependent invariant surface. This allows us to make a connection between the spectral problem at hand and the dimension theory of dynamical systems.engThis is an author's peer-reviewed final manuscript, as accepted by the publisher. The published article is copyrighted by Springer.Journal articlehttp://dx.doi.org/10.1007/s00039-012-0173-8