On non-QRT Mappings of the Plane

Nonlinear Sciences – Exactly Solvable and Integrable Systems

Scientific paper

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Scientific paper

We construct 9-parameter and 13-parameter dynamical systems of the plane
which map bi-quadratic curves to other bi-quadratic curves and return to the
original curve after two iterations. These generalize the QRT maps which map
each such curve to itself. The new families of maps include those that were
found as reductions of integrable lattices.

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