Recycling of strange sets: II. Applications
- 1 May 1990
- journal article
- Published by IOP Publishing in Nonlinearity
- Vol. 3 (2) , 361-386
- https://doi.org/10.1088/0951-7715/3/2/006
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.Keywords
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