Some more universal scaling laws for critical mappings View Full Text


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Article Info

DATE

1981-12

AUTHORS

P. Grassberger, M. Scheunert

ABSTRACT

We study such nonlinear mappingsxn+1=F(xn;bcr) of an intervalI into itself for which the Feigenbaum scaling laws hold (i.e., for which bcr is an accumulation point of bifurcation points). Letx0 be a random variable with some absolutely continuous distribution inI. We show in particular that (i) the geometric average distance ofxn from the nearest point of the attractor decreases liken−1.93387; (ii) the geometric average of ¦∂xn/∂x0¦ increases liken0.60; (iii) the geometric mean distance ¦xn−yn¦ between the iterates of two close-by pointsx0,y0 asymptotically tends towards a value ∼¦x0−y0¦0.77. These-and other-properties are also borne out from a simple probabilistic model which depicts the evolution as a random walklike process. More... »

PAGES

697-717

References to SciGraph publications

Identifiers

URI

http://scigraph.springernature.com/pub.10.1007/bf01010934

DOI

http://dx.doi.org/10.1007/bf01010934

DIMENSIONS

https://app.dimensions.ai/details/publication/pub.1014867078


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