Titlebook: Applications of Modern Dynamics to Celestial Mechanics and Astrodynamics; Proceedings of the N Victor Szebehely (L.B. Meaders Professor of

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Ergodic Theory and Area Preserving Mappingsfill a region in the plane having positive area. Such a region is called an “ergodic zone”. In this paper we give an exposition of some mathematical techniques which can be used to show that under suitable hypotheses, the closure of an orbit of a single point has positive Lebesque measure. We then a

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Exploding Dynamical Systems“explosion complexities” are discussed and the relationship between the stabilities and explosions are drawn. It is shown that a “stability index” in the sense of Poincare may be introduced to identify the stability of the characteristic solutions and used as a tool of global analysis of exploding s

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Howard Rasmussen,Irving L. Schwartzf libration is expressed as a function of the mass parameter and the normalized Jacobian constant. Brown’s conjecture regarding the termination of the tadpole branch of the family at L.is refined, and a heuristic proof of its validity is offered.

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Edward H. Blaine,Michael Rosenblattslowly varying parameters. The adiabatic invariant introduced in the context of quantum mechanics and of physics of nuclear particles is a very effective tool for the study of such problems..In this paper, we describe the basic ideas of this theory and apply it to the problem of capture into resonance of Titan and Hyperion.

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https://doi.org/10.1007/978-1-4614-8684-8s pointed out. It is also shown that the KAM invariants are regular invariants in the sense defined by Prigogine and his coworkers. Then, the relation between the ergodic problem and the KAM invariant is discussed.