β Scribed by Jaume Llibre; Kenneth R. Meyer; Jaume Soler
No coin nor oath required. For personal study only.
The linearization of the spatial restricted three body problem at the collinear equilibrium point L 2 has two pairs of pure imaginary eigenvalues and one pair of real eigenvalues so the center manifold is four dimensional. By the classical Lyapunov center theorem there are two families of periodic solutions emanating from this equilibrium point. Using normal form techniques we investigate the existence of bridges of periodic solutions connecting these two Lyapunov families. A bridge is a third family of periodic solutions which bifurcates from both the Lyapunov families. We show that for the mass ratio parameter + near 1Γ2 and near 0 there are many bridges of periodic solutions.
π SIMILAR VOLUMES
Single-frequency oscillations of a reversible mechanical system are considered. It is shown that the oscillation period of a non-linear system usually only depends on a single parameter and it is established that, at a critical point of the family, at which the derivative of the period with respect
The investigation of a distance-based regression model, using a one-dimensional set of equally spaced points as regressor values and I~ -y l as a distance function, leads to the study of a family of matrices which is closely related to a discrete analog of the Brownian-bridge stochastic process. We