Effective Reducibility of Quasiperiodic Linear Equations Close to Constant Coefficients Angel Jorba Rafael Ram Rez Ros and Jordi Villanueva

Effective Reducibility of Quasi-periodic Linear Equations Close to Constant Coefficients∗

Let us consider the differential equation ẋ = (A+ εQ(t, ε))x, |ε| ≤ ε0, where A is an elliptic constant matrix and Q depends on time in a quasi-periodic (and analytic) way. It is also assumed that the eigenvalues of A and the basic frequencies of Q satisfy a diophantine condition. Then it is proved that this system can be reduced to ẏ = (A∗(ε) + εR∗(t, ε))y, |ε| ≤ ε0, where R∗ is exponentially ...

Effective Stability around Periodic

On the Persistence of Lower Dimensional Invariant Tori under Quasiperiodic Perturbations

In this work we consider time dependent quasiperiodic perturbations of autonom ous Hamiltonian systems We focus on the e ect that this kind of perturbations has on lower dimensional invariant tori Our results show that under standard conditions of analyticity nondegeneracy and nonresonance most of these tori survive adding the frequencies of the perturbation to the ones they already have The pa...

Effective Stability around Periodic Orbits of the Spatial Rtbp Angel Jorba and Jordi Villanueva

In this work we study the dynamics around an elliptic periodic orbit of Hamiltonian systems To this end we have developped an algorithm to compute a normal form up to a nite order around this orbit that gives an accurate description of the dynamics close to it If the remainder of this normal form can be bounded it is not di cult to produce explicit bounds of the di usion time of trajectories st...

STABILITY AND ASYMPTOTIC BEHAVIOUR OF THE VERTICAL FAMILY OF PERIODIC ORBITS AROUND L OF THE RESTRICTED THREE BODY PROBLEM ANGEL JORBA and JORDI VILLANUEVA

In this note we present some numerical results about a family of periodic orbits of the Restricted Three Body Problem RTBP The family considered is one of the Lyapunov families related to the equlibrium point L More concretely we deal with the family related to the vertical oscillations around this point Here we present a study of the normal behaviour of this family for several values of the ma...