منابع مشابه
Integrable Non-qrt Mappings of the Plane
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 [11].
متن کاملFrom Integrable Lattices to Non-qrt Mappings
Second-order mappings obtained as reductions of integrable lattice equations are generally expected to have integrals that are ratios of biquadratic polynomials, i.e., to be of QRT-type. In this paper we find reductions of integrable lattice equations that are not of this type. The mappings we consider are exact reductions of integrable lattice equations proposed by Adler, Bobenko and Suris. Su...
متن کاملIntegrable mappings of the plane preserving biquadratic invariant curves II
We review recently introduced curve-dependent McMillan maps which are mappings of the plane that preserve biquadratic foliations. We show that they are measure preserving and thus integrable. We discuss the geometry of these maps including their fixed points and their stability. We consider the normal forms of symmetric and asymmetric biquadratic curves and the normal forms for their associated...
متن کاملThree Dimensional Integrable Mappings
We derive three-dimensional integrable mappings which have two invariants.
متن کاملIntegrable quantum mappings.
We discuss the canonical structure of a class of integrable quantum mappings, i.e. iterative canonical transformations that can be interpreted as a discrete dynamical system. As particular examples we consider quantum map-pings associated with the lattice analogues of the KdV and MKdV equations. These mappings possess a non-ultralocal quantum Yang-Baxter structure leading to the existence of co...
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ژورنال
عنوان ژورنال: Letters in Mathematical Physics
سال: 2009
ISSN: 0377-9017,1573-0530
DOI: 10.1007/s11005-009-0360-1