Geometric properties of quasiperiodic orbits of 2D Hamiltonian systems

By enforcing the isomorphism between the group SL(2, R ) and linear fractional transforms, this letter shows that, for quasi-periodic orbits of 2D area-preserving maps possessing regions of chaotic behavior, the vector tangent to the quasiperiodic orbit can be obtained from the dynamics of the associated linear fractional transforms (obtained from the differential of the map), which is Cesaro convergent. Several implications of this geometric result are addressed.