Fractal properties of critical invariant curves (Q1285262)

It is known that renormalization ideals also have been used to study the transition to chaos in two different situations which the authors examine in this paper. One comes from the disappearance of quasiperiodic motions in the case of critical circle maps. The second case is connected with the destruction of invariant tori for two-degree-of-freedom Hamiltonian systems. Here the authors study the fractal properties of the dynamics in both situations. The authors examine in particular the dimension of the invariant measure for some singular circe homeomorphisms for a variety of rotation numbers, through both the thermodynamic formalism and numerical computation.