Statistical properties of chaos demonstrated in a class of one-dimensional maps

Research output: Contribution to journalArticle

34 Citations (Scopus)

Abstract

One-dimensional maps with complete grammar are investigated in both permanent and transient chaotic cases. The discussion focuses on statistical characteristics such as Lyapunov exponent, generalized entropies and dimensions, free energies, and their finite size corrections. Our approach is based on the eigenvalue problem of generalized Frobenius-Perron operators, which are treated numerically as well as by perturbative and other analytical methods. The examples include the universal chaos function relevant near the period doubling threshold. Special emphasis is put on the entropies and their decay rates because of their invariance under the most general class of coordinate changes. Phase-transition-like phenomena at the border state of chaos due to intermittency and super instability are presented.

Original languageEnglish
Pages (from-to)31-49
Number of pages19
JournalChaos
Volume3
Issue number1
Publication statusPublished - 1993

Fingerprint

One-dimensional Maps
Chaos theory
Statistical property
chaos
Chaos
Entropy
Frobenius-Perron Operator
entropy
grammars
Generalized Dimensions
Change of coordinates
Generalized Entropy
Period Doubling
period doubling
Intermittency
intermittency
Invariance
borders
Decay Rate
Analytical Methods

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Physics and Astronomy(all)
  • Mathematical Physics
  • Applied Mathematics

Cite this

Statistical properties of chaos demonstrated in a class of one-dimensional maps. / Csordás, A.; Györgyi, G.; Szépfalusy, P.; Tél, T.

In: Chaos, Vol. 3, No. 1, 1993, p. 31-49.

Research output: Contribution to journalArticle

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