We show that for almost every ergodic S{integer dynamical system the radius of convergence of the dynamical zeta function is no larger than exp(? 1 2 htop) < 1. In the arithmetic case almost every zeta function is irrational. We conjecture that for almost every ergodic S{integer dynamical system the radius of convergence of the zeta function is exactly exp(?htop) < 1 and the zeta function is ir...

A model for ac-driven systems, based on the Tang-Wiesenfeld-Bak-Coppersmith-Littlewood automaton for an elastic medium, exhibits mode-locked steps with frequencies that are irrational multiples of the drive frequency, when the pinning is spatially quasiperiodic. Detailed numerical evidence is presented for the large-system-size convergence of such a mode-locked step. The irrational mode locking...

An interesting class of fractal sequences consists of signature sequences for irrational numbers. The signature sequence of the irrational number x is obtained by putting the numbers i + j × x i , j = 1, 2, 3, … in increasing order. Then the values of i for these numbers form the signature sequence for x, which is denoted by S(x). Here's the signature sequence for φ, the golden mean: Both upper...

We study the occurrence of physically observable phase locked states between chaotic oscillators and rotors in which the frequencies of the coupled systems are irrationally related. For two chaotic oscillators, the phenomenon occurs as a result of a coupling term which breaks the 2 pi invariance in the phase equations. In the case of rotors, a coupling term in the angular velocities results in ...

Jonathan St. B. T. Evans, in his engaging article “Rationality and the illusion of choice” (Evans, 2014) argues that erroneous answers to questions posed in the study of reasoning and decision-making (RDM) ought not be viewed as irrational, just as errors in other cognitive domains are not viewed as irrational. He attributes misuse of the term partly to use of normative models borrowed from eco...

Given any subset of Z we associate to it another set on which we can define one or more (generally independent) abstract factorial functions. These associated sets are studied and arithmetic relations are revealed. In addition, we show that for an abstract factorial function of an infinite subset of Z the series of reciprocals of its factorials is always an irrational number.

Due to the changes which may occur in their parameters, systems are usually demonstrated by some subsystems for different conditions. This paper employs Modified Petri Nets (MPN) to model theses subsystems and makes it simple to analyze them. In this method, first, the continuous transfer function is converted to a discrete transfer function and then, by MPN, system is modeled and analyzed. All...