Myers Hill, J, Sturman, R and Wilson, MCT orcid.org/0000-0002-1058-2003 (2022) A Family of Non-Monotonic Toral Mixing Maps. Journal of Nonlinear Science, 32 (3). 31. ISSN 0938-8974
Abstract
We establish the mixing property for a family of Lebesgue measure preserving toral maps composed of two piecewise linear shears, the first of which is non-monotonic. The maps serve as a basic model for the ‘stretching and folding’ action in laminar fluid mixing, in particular flows where boundary conditions give rise to non-monotonic flow profiles. The family can be viewed as the parameter space between two well-known systems, Arnold’s Cat Map and a map due to Cerbelli and Giona, both of which possess finite Markov partitions and straightforward to prove mixing properties. However, no such finite Markov partitions appear to exist for the present family, so establishing mixing properties requires a different approach. In particular, we follow a scheme of Katok and Strelcyn, proving strong mixing properties with respect to the Lebesgue measure on two open parameter spaces. Finally, we comment on the challenges in extending these mixing windows and the potential for using the same approach to prove mixing properties in similar systems.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © The Author(s) 2022. This is an open access article under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits unrestricted use, distribution and reproduction in any medium, provided the original work is properly cited. |
Keywords: | Low-dimensional dynamics, Non-uniform hyperbolicity, Mixing, Deterministic chaos |
Dates: |
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Institution: | The University of Leeds |
Academic Units: | The University of Leeds > Faculty of Engineering & Physical Sciences (Leeds) > School of Computing (Leeds) The University of Leeds > Faculty of Engineering & Physical Sciences (Leeds) > School of Mathematics (Leeds) > Applied Mathematics (Leeds) The University of Leeds > Faculty of Engineering & Physical Sciences (Leeds) > School of Mechanical Engineering (Leeds) > Institute of Engineering Thermofluids, Surfaces & Interfaces (iETSI) (Leeds) |
Depositing User: | Symplectic Publications |
Date Deposited: | 31 Mar 2022 13:09 |
Last Modified: | 30 May 2023 22:37 |
Status: | Published |
Publisher: | Springer Nature |
Identification Number: | 10.1007/s00332-022-09790-0 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:185263 |