Recycling of strange sets: II. Applications

Abstract

For pt.I see ibid., vol.3, no.2, p.325-59 (1990). Cycle expansions are applied to a series of low-dimensional dynamically generated strange sets: the skew Ulam map, the period-doubling repeller, the Henon-type strange sets and the irrational winding set for circle maps. These illustrate various aspects of the cycle expansion technique; convergence of the curvature expansions, approximations of generic strange sets by self-similar Cantor sets, effects of admixture of non-hyperbolicity, and infinite resummations required in presence of orbits of marginal stability. A new exact and highly convergent series for the Feigenbaum delta is obtained.