BOUNDARY CURVES FOR FAMILIES OF PLANAR ORBITS

For monoparametric families f(x, y) = c of planar orbits, created by a planar potential V(x, y), we introduce the notion of the family bound ary curves (FBC). All members of the family f(x, y) = c are traced in an allowable region of the xy plane, defined by the corresponding FBC, with total energy E = E(c) varying along the family. Family boundary curves are also found for two-parametric families f(x, y, b) = c. The relation of equilibrium points and asymptotic orbits, possibly possess ed by the potential V(x, y), to the FBC is studied.