Existence Criteria

  • Florin DiacuEmail author
Part of the Atlantis Series in Dynamical Systems book series (ASDS, volume 1)


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.


Differential Equation Dynamical System Angular Momentum Ordinary Differential Equation Formal Statement 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Copyright information

© Florin Diacu 2012

Authors and Affiliations

  1. 1.Department of Mathematics and StatisticsUniversity of VictoriaVictoriaCanada

Personalised recommendations