Period doubling in maps with a maximum of order z

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 → ∞.

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Year of publication:	1987
Authors:	Van Der Weele, J.P. ; Capel, H.W. ; Kluiving, R.
Published in:	Physica A: Statistical Mechanics and its Applications. - Elsevier, ISSN 0378-4371. - Vol. 145.1987, 3, p. 425-460
Publisher:	Elsevier

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Type of publication:	Article
Source:	RePEc - Research Papers in Economics

Persistent link: https://www.econbiz.de/10011059017