## Experimental Mathematics

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

### Scaling in a map of the two-torus

Gonzalo Álvarez and Keith M. Briggs

#### Abstract

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

**Source**

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

**Dates**

First available in Project Euclid: 22 February 2003

**Permanent link to this document**

https://projecteuclid.org/euclid.em/1045952353

**Mathematical Reviews number (MathSciNet)**

MR1780214

**Zentralblatt MATH identifier**

1106.37304

**Subjects**

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

#### Citation

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