Integrable Difference Analogue of the Logistic Equation and Bäcklund Transformation of the KP Hierarchy

Details Integrable Difference Analogue of the Logistic Equation and Bäcklund Transformation of the KP Hierarchy Integrable Difference Analogue of the Logistic Equation and Bäcklund Transformation of the KP Hierarchy

1994-10-24

arxiv.org/abs/hep-th/9410175v1

Physics

High Energy Physics

High Energy Physics - Theory

15 pages, Latex

Scientific paper

A difference analogue of the logistic equation, which preserves integrability, is derived from Hirota's bilinear difference equation. The integrability of the map is shown to result from the large symmetry associated with the B\"acklund transformation of the KP hierarchy. We introduce a scheme which interpolates between this map and the standard logistic map and enables us to study integrable and nonintegrable systems on an equal basis. In particular we study the behavior of Julia set at the point where the nonintegrable map passes to the integrable map.

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