Experimental Mathematics

Scaling in a map of the two-torus

Gonzalo Álvarez and Keith M. Briggs


We discuss scaling in the parameter space of a family of maps arising from the iteration of a map of the two-torus defined in terms of a Jacobian elliptic function. This map appears to show a complex analog of the Feigenbaum-Kadanoff-Shenker scaling found in bifurcation sequences of circle maps.

Article information

Experiment. Math. Volume 9, Issue 2 (2000), 301-307.

First available in Project Euclid: 22 February 2003

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 37F10: Polynomials; rational maps; entire and meromorphic functions [See also 32A10, 32A20, 32H02, 32H04]
Secondary: 37-04: Explicit machine computation and programs (not the theory of computation or programming) 37E99: None of the above, but in this section 37F50: Small divisors, rotation domains and linearization; Fatou and Julia sets


Briggs, Keith M.; Álvarez, Gonzalo. Scaling in a map of the two-torus. Experiment. Math. 9 (2000), no. 2, 301--307. https://projecteuclid.org/euclid.em/1045952353.

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