THE SPECTRUM OF THE PERIOD-DOUBLING OPERATOR IN TERMS OF CYCLES

The eigenvalue spectrum of the period-doubling operator is evaluated both in terms of unstable periodic orbits and by a diagonalisation at the operator. Cycles up to length ten yield the twelve leading eigenvalues; direct diagonalisation yields some 50 eigenvalues. The Feigenbaum delta , the Hausdorff dimension and the escape rate for the period-doubling repeller are evaluated to high accuracy.