Cremona transformation and general solution of one dynamical system of the static model
A particular quantum-physics problem is examined from an unusual point of view, because it is formulated in terms of an system of nonlinear difference equations. This system is considered to be equivalent to a second order quadratic Cremona map (QCM). Algebraic invariant curves of this QCM are determined explicitly. Short segments of two non-algebraic invariant curves crossing a saddle of the QCM are determined approximately by means of truncated series expansions. An asymptotic property of the latter is determined numerically. It is claimed that a general solution of the initial system has been constructed for one set of parameter values. An area preserving map is used in the argument without explaining how it is related qualitatively and quantitatively to an auxiliary dissipative map with a non-unity Jacobian.
system of nonlinear difference equations
scientific article; zbMATH DE number 94094