Complicated dynamics from simple topological hypotheses

Complicated dynamics from simple topological hypotheses. Arnold, V. I., Bruce, J. W., Moffatt, H. K., Pelz, R. B., & Mackay, R. S. Philosophical Transactions of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences, 359(1784):1479–1496, July, 2001. Publisher: Royal Society

Paper doi abstract bibtex

There are many types of dynamical system for which quite simple topological hypotheses 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.

@article{arnold_complicated_2001,
	title = {Complicated dynamics from simple topological hypotheses},
	volume = {359},
	url = {https://royalsocietypublishing.org/doi/abs/10.1098/rsta.2001.0849},
	doi = {10.1098/rsta.2001.0849},
	abstract = {There are many types of dynamical system for which quite simple topological hypotheses 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.},
	number = {1784},
	urldate = {2023-12-04},
	journal = {Philosophical Transactions of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences},
	author = {Arnold, V. I. and Bruce, J. W. and Moffatt, H. K. and Pelz, R. B. and Mackay, R. S.},
	month = jul,
	year = {2001},
	note = {Publisher: Royal Society},
	keywords = {chaos, dynamical systems, isotopy, markov partition, semiconjugacy, symbolic dynamics, 🔥},
	pages = {1479--1496},
}

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