Recycling of strange sets: II. Applications

Cycle expansions are applied to a series of low dimensional dynamically generated strange sets: the skew Ulam map, the period-doubling repeller, the H'enon-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 selfsimilar 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 ffi is obtained. 1 present address: Dipartimento di Fisica dell'Universit`a and I.N.F.N., Via Celoria 16, I-20133 Milano 2 Carlsberg Fellow 1 INTRODUCTION The goal of this paper is to demonstrate through a series of applications that description of low-dimensional chaotic systems in terms of unstable periodic orbits (cycles), advocated in the preceeding paper [1] (hereafter referred to as I), is not only feasi...