Giorgio Mantica

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An inverse problem in fractal set const ruc t ion is introduced in th is paper, according to the theory of iterated function systems (IFS) . This theory allows the construction of a class of fractals depending on a finite number of parameters. Finding a set of parameters which reconstructs a given fractal is the goal of the inverse problem. As the solution(More)
Hamiltonian tridiagonal matrices characterized by multi-fractal spectral measures in the family of Iterated Function Systems can be constructed by a recursive technique here described. We prove that these Hamiltonians are almost-periodic. They are suited to describe quantum lattice systems with nearest neighbours coupling, as well as chains of linear(More)
The global statistics of the return times of a dynamical system can be described by a new spectrum of generalized dimensions. Comparison with the usual multifractal analysis of measures is presented, and the difference between the two corresponding sets of dimensions is established. Theoretical analysis and numerical examples of dynamical systems in the(More)
A recursive technique for the determination of Jacobi matrices associated with multifractal measures generated via Iterated Functions Systems is described. This technique allows for the stable determination of large-rank matrices, a task for which the conventional approach, classical polynomial sampling, is proven here to be severely ill-conditioned.(More)
We study the Fourier transform of polynomials in an orthogonal family, taken with respect to the orthogonality measure. Mastering the asymptotic properties of these transforms, that we call Fourier–Bessel functions, in the argument, the order, and in certain combinations of the two is required to solve a number of problems arising in quantum mechanics. We(More)
Discretization of phase space usually nullifies chaos in dynamical systems. We show that if randomness is associated with discretization dynamical chaos may survive and be indistinguishable from that of the original chaotic system, when an entropic, coarse-grained analysis is performed. Relevance of this phenomenon to the problem of quantum chaos is(More)
We study the quantum dynamics of a charged particle in a two-dimensional lattice, subject to constant and homogeneous electric and magnetic fields. We find that different regimes characterize these motions, depending on a combination of conditions, corresponding to weak and strong electric field intensities, rational or irrational directions of the electric(More)