BCSSS

International Encyclopedia of Systems and Cybernetics

2nd Edition, as published by Charles François 2004 Presented by the Bertalanffy Center for the Study of Systems Science Vienna for public access.

About

The International Encyclopedia of Systems and Cybernetics was first edited and published by the system scientist Charles François in 1997. The online version that is provided here was based on the 2nd edition in 2004. It was uploaded and gifted to the center by ASC president Michael Lissack in 2019; the BCSSS purchased the rights for the re-publication of this volume in 200?. In 2018, the original editor expressed his wish to pass on the stewardship over the maintenance and further development of the encyclopedia to the Bertalanffy Center. In the future, the BCSSS seeks to further develop the encyclopedia by open collaboration within the systems sciences. Until the center has found and been able to implement an adequate technical solution for this, the static website is made accessible for the benefit of public scholarship and education.

A B C D E F G H I J K L M N O P Q R S T U V W Y Z

KAM THEOREMS 2)5)

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"KAM" is for the Russian mathematicians and physicists A.N. KOLMOGOROV, V.I. ARNOL'D and J. MOSER. The theorems are about the dynamics near a periodic orbit. They show that for some Hamiltonian systems (i.e., practically homeostatic) affected by slight perturbations, there may exist numerous different initial conditions that may produce quasi-periodic movements, describable by convergent series, and corresponding to toroidal attractors: The threshold of chaos can be, or not, crossed.

ARNOLD showed that this applies, at least in some cases when perturbations are quite small, to POINCARÉ's n-bodies problem.

For non-Hamiltonian systems, in I. PRIGOGINE's words: "KOLMOGOROV" (K-) systems exhibit a complex behavior of individual trajectories, like exponential divergence, to the effect that no finite algorithm can reliably compute the motion of phase points sensibly faster than the dynamics itself. Systems of this kind include geodesic flow on surfaces with negative curvature…" (1986, p.5).

K-FLOWS

(Also named after KOLMOGOROV)

K-flows are characteristic of near-chaotic systems. J. CASTI writes: "Their behavior is at the limit of unpredictability, in that having even an infinite number of measurements of where the system was in the past is of no help in predicting where it will be found next. K-flows are widespread among systems in which collisions between particles dominate the dynamics" (1990, p.288).

In synthesis, the borders between ergodic systems, thermodynamically unstable ones and chaotic ones are fuzzy.

→ Baker transformation and LIAPOUNOV exponent

Categories

  • 1) General information
  • 2) Methodology or model
  • 3) Epistemology, ontology and semantics
  • 4) Human sciences
  • 5) Discipline oriented

Publisher

Bertalanffy Center for the Study of Systems Science(2020).

To cite this page, please use the following information:

Bertalanffy Center for the Study of Systems Science (2020). Title of the entry. In Charles François (Ed.), International Encyclopedia of Systems and Cybernetics (2). Retrieved from www.systemspedia.org/[full/url]

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