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Universal scaling behaviour for iterated maps in the complex plane (1983)

Manton, N. S. ; Nauenberg, M.

Springer

Communications in mathematical physics 89 (1983), S. 555-570

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ISSN: 1432-0916

Source: Springer Online Journal Archives 1860-2000

Topics: Mathematics , Physics

Notes: Abstract According to the theory of Schröder and Siegel, certain complex analytic maps possess a family of closed invariant curves in the complex plane. We have made a numerical study of these curves by iterating the map, and have found that the largest curve is a fractal. When the winding number of the map is the golden mean, the fractal curve has universal scaling properties, and the scaling parameter differs from those found for other types of maps. Also, for this winding number, there are universal scaling functions which describe the behaviour asn→∞ of theQ n th iterates of the map, whereQ n is then th Fibonacci number.

Type of Medium: Electronic Resource

URL: http://dx.doi.org/10.1007/BF01214743

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