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Preface
Basic notation
Introduction
Mathematical means
The normal form of a Hamiltonian system
The normal form of a linear system
Nonlinear normalization
Lowering the number of degrees of freedom
Periodic and conditionally-periodic solutions
Generalizations
Notes
Normalization of a Hamiltonian system near a cycle or a torus
The normal form of a linear Hamiltonian system with periodic coefficients
The normal form in a neighbourhood of a periodic solution
The neighbourhood of an invariant torus
A system with two degrees of freedom
Notes
Solutions of the limiting problem (μ = 0)
Periodic solutions and arc solutions
Formulation of the restricted three-body problem
The two-body problem
The restricted three-body problem for μ = 0
Notes
Properties of arc solutions of the families S and TN
Orbits of the families S
The structure of the set of characteristics of the families S and TN
Values of the Jacobian constant
Notes
Extrema of the Hamiltonian function on families of arc solutions
The function G
Partial derivatives of the function G
Classification of the segments of the characteristics
Estimation of the number of intersections of a segment of a characteristic with a level line of the function G
The domain ρ3
Conclusion
Trajectories of collisions
The problem of two bodies P1 and P3
Trajectories of collision with P2
Arc solutions with consecutive collisions
Isolation of critical solutions
Notes
Regular generating solutions
Solutions of the second kind
Sets of periodic solutions
The restricted three-body problem
Averaging of the perturbing function
Computation of generating families
Concerning the programs
Other properties of the families EN
Limits of generating families
Conditionally-periodic solutions of the second kind
Notes
Solutions of the first kind
Reduction to the normal form
Integration of the normal form for rational λ = p̃̃/q̃̃
Application to the restricted problem
Conclusion
The neighbourhood of stationary points
Notes
Generating arc solutions from C¯1C¯1
Generating solutions of collisions with P1
Computation of families of generating arc solutions
Asymptotics of families of generating arc solutions
Concerning periodic solutions with collisions
Notes
Perturbations of hyperbolic orbits
The normal form
Application to the restricted problem
Notes
Appendix. Tables of generating families and their perturbations
Bibliography
Author index
Subject index