Cristel CHANDRE

Laboratoire de Physique
Universite de Bourgogne
B.P. 400 F- 21011 Dijon
France
cchandre@jupiter.u-bourgogne.fr

Critical strange attractor of an approximate renormalization-group scheme for quasi-periodically driven rotators

Abstract : We study an approximate renormalization-group transformation to analyze the breakup of invariant tori for three dimensional Hamiltonian systems. Two basic approximations are involved in this transformation: we truncate the Hamiltonians to quadratic order in the action variables, and we neglect all the Fourier modes except the three most relevant ones at each iteration of the transformation. The scheme is implemented for the spiral mean torus. We find numerically that the critical surface is the stable manifold of a critical strange attractor. We compute some scaling exponents associated with this fixed set, and find that they can be expected to be universal.