Space Manifold Dynamics pp 113-132 | Cite as

# Regular and Chaotic Dynamics of Periodic and Quasi-Periodic Motions

## Abstract

We review some basic topics from Dynamical System theory, which are of interest in Space Manifold Dynamics. We start by recalling some notions related to equilibrium points. Floquet theorem leads to the introduction of Lyapunov exponents. Nearly–integrable systems are very common in Celestial Mechanics; their study motivated the development of perturbation theories as well as of KAM and Nekhoroshev’s theorem. The Lindstedt–Poincaré technique allows to look for periodic orbits. Finally, we recall the derivation of the Lagrangian points in the circular and elliptic, planar, restricted three–body problem. Each section is *almost* self–contained and can be read independently from the others.

## Keywords

Lyapunov Exponent Unstable Manifold Body Problem Center Manifold Lagrangian Point## References

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