In this paper we present a numerical method to compute Diophantine rotation numbers of circle maps with high accuracy. We mainly focus on analytic circle diffeomorphisms, but the method also works inâ€¦ (More)

The purpose of this paper is to study the dynamics near a reducible lower dimen sional invariant tori of a nite dimensional autonomous Hamiltonian system with degrees of freedom We will focus in theâ€¦ (More)

In this paper we introduce a general methodology for computing numerically the normal form around a periodic orbit of an autonomous analytic Hamiltonian system The process follows two steps First weâ€¦ (More)

We consider the Arnold Tongue of the Arnold family of circle maps associated to a fixed Diophantine rotation number Î¸ . The corresponding maps of the family are analytically conjugate to a rigidâ€¦ (More)

We present a new approach to the numerical computation of the basic frequencies of a quasiperiodic signal. Although a complete toolkit for frequency analysis is presented, our methodology is betterâ€¦ (More)

Let us consider the differential equation áº‹ = (A + ÎµQ(t, Îµ))x, |Îµ| â‰¤ Îµ0, where A is an elliptic constant matrix and Q depends on time in a quasi-periodic (and analytic) way. It is also assumed thatâ€¦ (More)

In this paper we present a numerical method to compute deriva tives of the rotation number for parametric families of circle diffeomorphisms w ith high accuracy. Our methodology is an extension of aâ€¦ (More)

The paper deals with different kinds of invariant motions (periodic orbits, 2D and 3D invariant tori and invariant manifolds of periodic orbits) in order to analyze the Hamiltonian direct Hopfâ€¦ (More)

Recently, a new numerical method has been proposed to comput e rota ion numbers of analytic circle diffeomorphisms, as well as derivatives wi th respect to parameters, that takes advantage of theâ€¦ (More)

We study elliptic lower dimensional invariant tori of Hamiltonian systems via parame terizations. The method is based in solving iteratively the functional equations that tand for invariance andâ€¦ (More)