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| Thermodynamic formalism is a powerful technique that provides many insights to the dynamical properties of hyperbolic maps. Using the connections between spectral characteristics of Fibonacci Hamiltonian (such as optimal H\"older exponent of the integrated density of states, dimensions of the spectrum and of the density of states measure, and upper transport exponents) and dynamical characteristics of the Fibonacci trace map, we apply the thermodynamic formalism techniques to establish strict inequalities between the spectral characteristics for all non-zero values of the coupling constant. In particular, this proves a conjecture on non-coincidence of the dimension of the spectrum and the dimension of the density of states measure stated by Barry Simon. The results are joint with David Damanik and William Yessen. |
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