  The so-called "anemone" solar flares are an interesting type of the space
plasma phenomena, where multiple null points of the magnetic field are
connected with each other and with the magnetic sources by the separators,
thereby producing the complex branching configurations. Here, using the methods
of dynamical systems and Morse-Smale theory, we derive a few universal
topological relations between the numbers of the null points and sources of
various kinds with arbitrary arrangement in the above-mentioned structures.
Such relations can be a valuable tool both for a quantification of the
already-observed anemone flares and for a prediction of the new ones in complex
magnetic configurations.
