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The purpose of this paper is to illustrate the many aspects of Poincare recurrence time theorem for an archetype of a complex system, the logistic map.

At the beginning of the twentieth century, Poincare's recurrence theorem had revolutionized modern mechanics and statistical physics. However, this theorem did not attract considerable attention, at least from a numerical and computational point of view. In a series of relatively recent papers, Balakrishnan, Nicolis and Nicolis have addressed the recurrence time problem in a firm basis, introducing notation, theory, and numerical studies. Motivated by this call, the paper proposes to illustrate the many aspects of Poincare recurrence time theorem for an archetype of a complex system, the logistic map. The authors propose here in different tests and computations, each one illuminating the many aspects of the problem of recurrence. The paper ends up with a short discussion and conclusions.

In this paper, the authors obtain new results on computations, each one illuminating the many aspects of the problem of recurrence. One striking aspect of this detailed work, is that when the sizes of the cells in the phase space became considerable, then the recurrence times assume ordinary values.

The paper extends previous results on chaotic maps to the logistic map, enhancing comprehension, making possible connections with number theory, combinatorics and cryptography.

Given a time‐series, what is the best partitioning of the state space in order to obtain reasonable values for the block entropies? The purpose of this paper is to provide a simple answer (an algorithm), although approximative, in connection with symbolic dynamics and statistical properties of 1‐d maps on the interval.

The logistic map is examined as an archetype of a Complex System with different behaviors, namely: periodicity, order‐to‐chaos period‐doubling transition, weak chaos, parametric intermittent chaos, developed chaos and fully developed chaos. For the logistic map the generating partition is known, and allows comparison with other prescriptions in the literature. The partitioning of the phase space with the easy generated bipartition induced by the mean value of a curve in the plane, gives results in good agreement (roughly up to a 20 per cent difference) with the results of the generating partition, if the trajectory of the system is in parametric intermittent chaos and in developed chaos (DC). In the case of fully developed chaos (FDC), the agreement is perfect.

The authors confirm that a statistical partitioning is almost equivalent with the exact partitioning for the logistic map.

The paper updates previous results and proposes a better understanding on the partitioning for symbolic dynamics.

The purpose of this paper is to present a vision for the future development of Kybernetes under a new editorship.

The new Editors are introduced, the strengths and history of the journal reviewed, and plans for its future development described.

The future of Kybernetes will build on its long and distinguished heritage, noting especially the strengths of interdisplinarity, internationality, and strong links with major cybernetic societies across the world. While maintaining these strengths, the new Editors will seek to develop further the conversations between diverse fields contributing to the journal and to bring a new emphasis to the interdisciplinary study of information, to studies of the social implications of cybernetics and related fields, and to profiles of thinkers in cybernetics, systems and management science.

This is only the second time that there has been a change of editor in the more than 40 years that Kybernetes has been published. The journal (and the whole field of cybernetics and systems) owes the past editors a great debt of thanks for their outstanding work, but the time has come for change. This paper starts to identify new directions under the new Editors.