REGULAR ORBITS AND PERIODIC LOOPS IN MULTIPLY BARRED GALACTIC POTENTIALS

We show that nonchaotic multiply periodic particle orbits can exist in a galaxy-like potential where a small, fast-tumbling nuclear bar is n ested inside a main bar that has a slower pattern speed. We introduce the concept of a loop: a one-dimensional curve such that particles dis tributed along it at some initial instant return to the same curve (as viewed in the rotating frame of one of the bars) after the bars retur n to the same relative position. Just as particles following regular o rbits in a simply barred potential are trapped around closed periodic orbits, so regular orbits in a doubly barred potential oscillate about stable loops. We find both loops that remain aligned with the inner b ar and loops aligned with the outer bar: particles trapped around thes e loops could form the building blocks for a long-lived, self-consiste nt, doubly barred galaxy. In a realistic doubly barred galaxy potentia l, we demonstrate the existence of stable loops that support the struc ture of the inner bar. We use the epicyclic approximation to preview t he pattern of gas flow in a doubly barred potential.