A complete list of combinations of the rates of asteroid perihelia and nodes and the corresponding fundamental frequencies of planets, giving rise to secular resonances and involving up to 4 frequencies, is known from the previous work, while for the resonances with 6 frequencies a systematically derived comprehensive list is given here for the first time. There are 28 divisors in the theory of degree up to 4, not all of which can give rise to resonances, while at degree 6 there are (at least) 33 such possibly resonant frequency combinations.

Mapping the secular resonances by plotting the resonant lines in the phase space of proper elements or of secular frequencies, possibly also against the background of known asteroids, enables to straightforwardly identify resonances causing large long periodic variations of asteroid orbital elements, resonances that interact with known families, those that bound the dynamically distinct regions, deplete or disturb asteroids in these regions, etc.

We present the results of a study of secular resonances in a binary star system and their effects on the formation of terrestrial planets. The systems of our interest are binaries with moderate separations (i.e., smaller than 40 AU) where planets revolve around one of the stars. Using numerical simulations, we demonstrate the appearance and evolution of secular resonances in systems with two giant planets. Results indicate that the perturbation of the binary companion suppresses secular resonances and they do not play a significant role on the formation and orbital architecture of terrestrial planets. Unlike in our solar system where the secular resonance of Saturn confines the formation of terrestrial planets to regions interior to its location, in a binary star, terrestrial planets can form interior and exterior to this resonance. We present details of our simulations and discuss the implications of their results.