Polynomial ideals and symmetries of quadratic dynamical systems


主讲人:Professor Tatjana Petek,University of Maribor




内容介绍:One of the important problems arising in the investigation of the qualitative  behavior of dynamical systems is determining whether a given system admits some  kind of symmetry. In studies of dynamical systems described by autonomous  polynomial systems of ordinary differential equations, we deal mainly with two  kinds of symmetries: the rotational symmetry (Zq-symmetry) and the  time-reversible (involutive) symmetry. The existence of time-reversibility in a  polynomial system is closely related to the integrability of the system and  rotational symmetries have a connection to the second part of Hilbert's 16th  problem. For a given family of real planar polynomial systems of ordinary  differential equations depending on parameters, we consider the problem of how  to find the systems in the family which become symmetric after some affine (i.e.  linear + translation) transformation of the coordinate system. We present the  solution in the form of algebraic varieties in the space of parameters.