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In this chapter we establish criteria for the existence of positive elliptic and elliptic-elliptic as well as negative elliptic, hyperbolic, and elliptic-hyperbolic RE. These criteria will be employed in later chapters to obtain concrete examples of such orbits. The proofs are similar in spirit, but for completeness and future reference we describe them all since the specifics differ in each case. We close this chapter by showing that negative parabolic RE do not exist in the curved N-body problem.
KeywordsDifferential Equation Dynamical System Angular Momentum Ordinary Differential Equation Formal Statement
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