Orbits in Highly Perturbed Dynamical Systems. I. Periodic Orbits
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Abstract
Periodic orbits are the main "landmarks" in the study of perturbed dynamical systems. We find the characteristic curves of many families of periodic orbits in a "galactic-type" potential with increasing perturbation. There are two types of families: (a) regular families which are generated (directly or through intermediate families) from the unperturbed system, and (b) irregular ones, which are independent of the above. The appearance of irregular families of periodic orbits seems to be connected with the "dissolution" of the invariant curves of nearby nonperiodic orbits. The number of families crossing the x axis a given number of times increases considerably as the perturbation increases, especially beyond the escape pertur- bation, near the escape regions. All families seem to continue to exist as the perturbation increases and tends to infinity.
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