A particular periodic orbit in the Earth-Sun circular restricted three body problem is shown to have the characteristics needed for a ballistic lunar capture transfer. An injection from a circular parking orbit into the periodic orbit serves as an initial guess for a targeting algorithm. By targeting appropriate parameters incrementally in increasingly complicated force models and using precise...

We consider a class of simple quasi one-dimensional classically non-integrable systems which capture the essence of the periodic orbit structure of general hy-perbolic nonintegrable dynamical systems. Their behavior is simple enough to allow a detailed investigation of both classical and quantum regimes. Despite their classical chaoticity, these systems exhibit a " nonintegrable analog " of the...

This paper studies how to construct orbit transfers, chains, and complex periodic orbits in the planar circular restricted three-body problem using the invariant manifolds of unstable three-body orbits. It is shown that the Poincaré map is a useful tool to identify and construct transfer trajectories from one orbit to another, i.e., homoclinic and heteroclinic orbit connections, with applicatio...

A new transition mechanism to Alfvén chaos via boundary crisis is reported. This crisis appears in a complex plasma region in the presence of a large number of coexisting attractors. We characterize an example of double boundary crises using the unstable periodic orbit determined from the numerical solution of the driven-dissipative derivative nonlinear Schrödinger equation, and demonstrate how...

We investigate the convergence towards periodic orbits in discrete dynamical systems. We examine the probability that a randomly chosen point converges to a particular neighborhood of a periodic orbit in a fixed number of iterations, and we use linearized equations to examine the evolution near that neighborhood. The underlying idea is that points of stable periodic orbit are associated with in...

We review some properties of periodic orbit families in polygonal billiards and discuss in particular a sum rule that they obey. In addition, we provide algorithms to determine periodic orbit families and present numerical results that shed new light on the proliferation law and its variation with the genus of the invariant surface. Finally, we deal with correlations in the length spectrum and ...

On the other hand, let S be a subset of the real numbers and let / be a function from S into itself. For every positive integer n, we let f denote the n iterate of f : f =f and f=f<> f~ for n > 2. For every #0 G s > w e call the set {f(xQ)\k > 0} the orbit of xQ under /. If XQ satisfies f{x$) = XQ for some positive integer 77?, then we call XQ a periodic point of / and call the smallest such po...

The level statistics of pseudointegrable fractal drums is studied numerically using periodic orbit theory. We find that the spectral rigidity ∆3(L), which is a measure for the correlations between the eigenvalues, decreases to quite small values (as compared to systems with only small boundary roughness), thereby approaching the behavior of chaotic systems. The periodic orbit results are in goo...

We generalize the sufficient condition for the stability of relative periodic orbits in symmetric Hamiltonian systems presented in [J.-P. Ortega, T.S. Ratiu, J. Geom. Phys. 32 (1999) 131-1591 to the case in which these orbits have non-trivial symmetry. We also describe a block diagonalization, similar in philosophy to the one presented in [J.-P. Ortega, T.S. Ratiu, Nonlinearity 12 (1999) 693720...

We consider an analytic Hamiltonian system with three degrees of freedom and having a family of periodic orbits with a transition stability complex instability We reduce the Hamiltonian to a normal form around a transition periodic orbit and we obtain H Z r R r The analysis of the truncated normal form Z r allows the description of a Hopf bifurcation of D tori However this communication will co...