Period doubling in maps with a maximum of order z

J.P. Van Der Weele, H.W. Capel and R. Kluiving

Physica A: Statistical Mechanics and its Applications, 1987, vol. 145, issue 3, 425-460

Abstract: We consider the scaling behaviour in period-doubling systems, exemplified by the one-dimensional map χn+1 = 1 − λ|χn|z, which has a maximum of order z (z > 1). The Feigenbaum scaling factors α and δ are studied as functions of z, and more generally the scaling functions 1/σ and ƒ(a). In particular, using the universal functions g(x) and h(x) we establish the inequality δ < αz, which implies that δ remains finite (≲ 30) in the limit z → ∞.

Date: 1987
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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:145:y:1987:i:3:p:425-460

DOI: 10.1016/0378-4371(87)90004-5

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