We examine the connectivity fluctuations across networks obtained when the horizontal visibility (HV) algorithm is used on trajectories generated by nonlinear circle maps at the quasiperiodic transition to chaos. The resultant HV graph is highly anomalous as the degrees fluctuate at all scales with amplitude that increases with the size of the network. We determine families of Pesin-like identi...

The von Neumann entropy production for a quantum mechanical kicked rotor coupled to a thermal environment is calculated. This rate of entropy increase is shown to be a good criterion to distinguish between quantum mechanical counterparts of chaotic and regular classical motion. We show that for high temperatures the entropy production rate increases linearly with the Kolmogorov-Sinai entropy of...

A novel class of graphs, here named quasiperiodic, are constructed via application of the Horizontal Visibility algorithm to the time series generated along the quasiperiodic route to chaos. We show how the hierarchy of mode-locked regions represented by the Farey tree is inherited by their associated graphs. We are able to establish, via Renormalization Group (RG) theory, the architecture of t...

We analyze the Rosenblatt process which is a selfsimilar process with stationary increments and which appears as limit in the so-called Non Central Limit Theorem (Dobrushin and Major (1979), Taqqu (1979)). This process is non-Gaussian and it lives in the second Wiener chaos. We give its representation as a Wiener-Itô multiple integral with respect to the Brownian motion on a finite interval and...

The logistic map is one of the simple systems exhibiting order to chaos transition. In this work we have investigated the possibility of using the logistic map in the chaotic regime (logmap) for a pseudo random number generator. To this end we have performed certain statistical tests on the series of numbers obtained from the logmap. We find that the logmap passes these tests satisfactorily and...

In this paper, we use mathematical tools developed for chaos theory and time series analysis and apply them to the analysis and resynthesis of musical instruments. In particular, we can embed a basic one-dimensional audio signal time series within a higher-dimensional space to uncover the underlying generative attractor. Röbel [7],[8] described a neural-net model for audio sound synthesis based...

We develop a de nition of equilibrium for agenda formation in general voting settings. The de nition is independent of any protocol. We show that the set of equilibrium outcomes for any Pareto eÆcient voting rule is uniquely determined, and in fact coincides with that of the outcomes generated by considering all full agendas. Under voting by successive elimination (or amendment), the set of equ...

A discussion about dependences of the (fractal) basin boundary dimension with the definition of the basins and the size of the exits is presented for systems with one or more exits. In particular, it is shown that the dimension is largely independent of the choice of the basins, and decreases with the size of the exits. Considering the limit of small exits, a strong relation between fractals in...

The asymptotic distance between trajectories d∞, is studied in detail to characterize the occurrence of chaos. We show that this quantity is quite distinct and complementary to the Lyapunov exponents, and it allows for a quantitave estimate for the folding mechanism which keeps the motion bounded in phase space. We study the behaviour of d∞ in simple unidimensional maps. Near a critical point d...