Задача Эрдеша – Вершика для золотого сечения
Properties of Erdos measure and the invariant Erdos measure for the golden ratio and all values of the Bernoulli parameter are studies. It is proved that a shift on the two-sided Fibonacci compact set with invariant Erdos measure is isomorphic to the integral automorphism for a Bernoulli shift with countable alphabet. An effective algorithm for calculating the entropy of an invariant Erdos measure is proposed. It is shown that, for certain values of the Bernulli parameter, the algorithm gives the Hausdorff dimension of an Erdos measure to 15 decimal places.