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The apsidal precession frequency in a fixed gravitational potential increaseswith the radial range of the orbit (eccentricity). Although the frequencyincrease is modest it can have important implications for wave dynamics ingalaxy discs, which have not been previously explored in detail. One of themost interesting consequences is that for a given pattern frequency, eachLindblad resonance does not exist in isolation, but rather is the parent of acontinuous sequence of resonant radii, a Lindblad Zone, with each radius inthis zone characterized by a specific eccentricity. In the epicyclicapproximation the precession or epicyclic frequency does not depend on epicyclesize, and this phenomenon is not captured. A better approximation for eccentricorbits is provided by p-ellipse curves (Struck 2006), which do exhibit thiseffect. Here the p-ellipse approximation and precession-eccentricity relationare used as tools for finding the resonant radii generated from variousLindblad parent resonances. Simple, idealized examples, in flat rotation curveand near solid-body discs, are used to show that ensembles of eccentricresonant orbits excited in Lindblad Zones can provide a backbone for generatinga variety of (kinematic) bars and spiral waves. In cases balancingradius-dependent circular frequencies and eccentricity-dependent precession, arange of resonant orbits can maintain their form in the pattern frame, and donot wind up. Eccentric resonance orbits require a strong perturbation to excitethem, and may be produced mostly in galaxy interactions or by strong internaldisturbances.

Lindblad Zones: resonant eccentric orbits to aid bar and spiral formation in galaxy discs