Integrable Non-QRT Mappings of the Plane

  • Pavlos Kassotakis
  • Nalini Joshi


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 by Joshi et al. (Lett. Math. Phys. 78:27–37, 2006).

Mathematics Subject Classification (2000)

39A12 37J35 37J15 


integrable mappings QRT/non-QRT mappings integration 


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Copyright information

© Springer 2009

Authors and Affiliations

  1. 1.School of Mathematics and Statistics F07The University of SydneySydneyAustralia

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