主講人：Professor Tatjana Petek,University of Maribor
內容介紹：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.