Order in Binary Sequences and the Routes to Chaos

The natural order in the space of binary sequences permits to recover the $U$-sequence. Also the scaling laws of the period-doubling cascade and the intermittency route to chaos defined in that ordered set are explained. These arise as intrinsic properties of this ordered set, and independent from any consideration about dynamical systems.Comment: 13 pages, 2 table

Study of a model for the distribution of wealth

An equation for the evolution of the distribution of wealth in a population of economic agents making binary transactions with a constant total amount of "money" has recently been proposed by one of us (RLR). This equation takes the form of an iterated nonlinear map of the distribution of wealth. The equilibrium distribution is known and takes a rather simple form. If this distribution is such that, at some time, the higher momenta of the distribution exist, one can find exactly their law of evolution. A seemingly simple extension of the laws of exchange yields also explicit iteration formulae for the higher momenta, but with a major difference with the original iteration because high order momenta grow indefinitely. This provides a quantitative model where the spreading of wealth, namely the difference between the rich and the poor, tends to increase with time.Comment: 12 pages, 2 figure

Detecting synchronization in spatially extended discrete systems by complexity measurements

The synchronization of two stochastically coupled one-dimensional cellular automata (CA) is analyzed. It is shown that the transition to synchronization is characterized by a dramatic increase of the statistical complexity of the patterns generated by the difference automaton. This singular behavior is verified to be present in several CA rules displaying complex behavior.Comment: 4 pages, 2 figures; you can also visit http://add.unizar.es/public/100_16613/index.htm

Number and Amplitude of Limit Cycles emerging from {\it Topologically Equivalent} Perturbed Centers

We consider three examples of weekly perturbed centers which do not have {\it geometrical equivalence}: a linear center, a degenerate center and a non-hamiltonian center. In each case the number and amplitude of the limit cycles emerging from the period annulus are calculated following the same strategy: we reduce of all of them to locally equivalent perturbed integrable systems of the form: $dH(x,y)+\epsilon(f(x,y)dy-g(x,y)dx)=0$, with $H(x,y)={1/2}(x^2+y^2)$. This reduction allows us to find the Melnikov function, $M(h)=\int_{H=h}fdy-gdx$, associated to each particular problem. We obtain the information on the bifurcation curves of the limit cycles by solving explicitly the equation $M(h)=0$ in each case.Comment: 17 pages, 0 figure

A method to discern complexity in two-dimensional patterns generated by coupled map lattices

Complex patterns generated by the time evolution of a one-dimensional digitalized coupled map lattice are quantitatively analyzed. A method for discerning complexity among the different patterns is implemented. The quantitative results indicate two zones in parameter space where the dynamics shows the most complex patterns. These zones are located on the two edges of an absorbent region where the system displays spatio-temporal intermittency.Comment: 3 pages, 3 figures; some information about the authors: http://add.unizar.es/public/100_16613/index.htm

Statistical complexity, Fisher-Shannon information, and Bohr orbits in the H-atom

The Fisher-Shannon information and a statistical measure of complexity are calculated in the position and momentum spaces for the wave functions of the H-atom. For each level of energy, it is found that these two indicators take their minimum values on the orbitals that correspond to the classical (circular) orbits in the Bohr atomic model, just those with the highest orbital angular momentum.Comment: 7 pages, 2 figure