Journal
PHILOSOPHICAL TRANSACTIONS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES
Volume 359, Issue 1784, Pages 1479-1496Publisher
ROYAL SOC
DOI: 10.1098/rsta.2001.0849
Keywords
dynamical systems; chaos; Markov partition; symbolic dynamics; semiconjugacy; isotopy
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There are many types of dynamical system for which quite simple topological hy potheses imply very complicated behaviour. A well-known example is 'period 3 implies chaos' for continuous maps of an interval. A diverse range of more sophisticated examples has been produced by; many researchers and is reviewed here. The relevance to physical applications - like mixing in fluid flows. chaotic motion of mechanical linkages, and fast dynamos - is explored.
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