652 research outputs found
On the construction of elliptic solutions of integrable birational maps
This is an Accepted Manuscript of an article published by Taylor & Francis in “Experimental mathematics” on 24th August 2016, available online: http://www.tandfonline.com/doi/full/10.1080/10586458.2016.1166354We present a systematic technique to find explicit solutions of birational maps, provided that these solutions are given in terms of elliptic functions. The two main ingredients are the following: (i) application of classical addition theorems for elliptic functions and (ii) experimental technique to detect an algebraic curve containing a given sequence of points in a plane. These methods are applied to Kahan–Hirota–Kimura discretizations of the periodic Volterra chains with three and four particles.Peer ReviewedPostprint (author's final draft
On 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
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