We describe a renormalization group transformation that is related to the breakup of golden invariant tori in Hamiltonian systems with two degrees of freedom. This transformation applies to a large class of Hamiltonians, is conceptually simple, and allows for accurate numerical computations. In a numerical implementation, we find a nontrivial fixed point and determine the corresponding critical...

Answer to cond-mat/0106005, cond-mat/0106006 and additional notes are given concerning my previous comment (cond-mat/0105325). Recently I have discussed the numerical results for the Anderson transition [1]. Objections [2] and [3] have appeared after that. We answer here to the arguments of [2, 3] and give the additional comments. 1. First of all, some explanations. Indeed, I used two strong ex...

The Metropolis algorithm [8] is a mainstay of scientific computing. Indeed it appears first on a list of the “Top Ten Algorithms” [12]. It gives a method for sampling from probability distributions on high-dimensional spaces when these distributions are only known up to a normalizing constant. For background and references to extensive applications in physics, chemistry, biology and statistics,...