Unpredictable points and chaos


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AKHMET M., Fen M. O.

COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION, vol.40, pp.1-5, 2016 (Peer-Reviewed Journal) identifier identifier

  • Publication Type: Article / Article
  • Volume: 40
  • Publication Date: 2016
  • Doi Number: 10.1016/j.cnsns.2016.04.007
  • Journal Name: COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION
  • Journal Indexes: Science Citation Index Expanded, Scopus
  • Page Numbers: pp.1-5
  • Keywords: Unpredictable point, Poincarechaos, Quasi-minimal set, Symbolic dynamics, COMPUTER-ASSISTED PROOF, EQUATIONS

Abstract

It is revealed that a special kind of Poisson stable point, which we call an unpredictable point, gives rise to the existence of chaos in the quasi-minimal set. The existing definitions of chaos are formulated in sets of motions. This is the first time in the literature that description of chaos is initiated from a single motion. The theoretical results are exemplified by means of the symbolic dynamics. (C) 2016 Elsevier B.V. All rights reserved.