Abstract
This paper considers the formation of stellar galactic structures, which are assumed to be slow modes in a disc of orbits precessing at different speeds. The mode pattern speeds, Ωp, are eigen-values of a Fredholm integral operator. Its general analysis shows the existence of two types of eigen-functions, bar-like and spiral. The bars grow through the immediate action of mode gravitational fields on the stars near the corotation and the outer Lindblad resonance. The excitation of spirals is due to the inner Lindblad resonance. Apparently, the commonly used swing amplification mechanism does not play any role in the formation of both bar-modes and grand design spiral modes. However, it can be essential in the formation of transient excitations when the normal global mode cannot be organized.
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