Unpredictable points and chaos
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION, vol.40, pp.1-5, 2016 (SCI-Expanded, Scopus)
- 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 (SCI-EXPANDED), Scopus
- Page Numbers: pp.1-5
- Keywords: Unpredictable point, Poincarechaos, Quasi-minimal set, Symbolic dynamics, COMPUTER-ASSISTED PROOF, EQUATIONS
- Open Archive Collection: AVESIS Open Access Collection
- TED University Affiliated: No
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.