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Dependence of universal constants upon multiplication period in nonlinear maps

journal contribution
posted on 2023-05-18, 04:57 authored by Robert DelbourgoRobert Delbourgo, Hart, W, Kenny, BG
Noninvertible one-dimensional maps with cycle periods undergoing multiplication by a factor N, as a result of (tangent) bifurcation, are governed by map-independent universal constants αNαN,δNδN as the parameter λ of the map approaches the point of accumulation λN∞λN. By explicit computation, we have determined the constants for all cycle structures and all values of N up to 7 (and in addition for many cycles up to N=11). We find that the relation between α and δ is roughly independent of the detailed cycle structure and follows quite well the Eckmann-Epstein-Wittwer asymptotic prediction that 3δ=2α2α2. .AE

History

Publication title

Physical Review A

Volume

31

Pagination

514-516

ISSN

1050-2947

Department/School

School of Natural Sciences

Publisher

American Physical Soc

Place of publication

One Physics Ellipse, College Pk, USA, Md, 20740-3844

Repository Status

  • Restricted

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