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How many inflections are there in the Lyapunov spectrum?
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Jenkinson, O., Pollicott, Mark and Vytnova, Polina (2021) How many inflections are there in the Lyapunov spectrum? Communications in Mathematical Physics, 386 (3). pp. 1383-1411. doi:10.1007/s00220-021-04161-4 ISSN 0010-3616.
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Official URL: https://doi.org/10.1007/s00220-021-04161-4
Abstract
Iommi and Kiwi (J Stat Phys 135:535–546, 2009) showed that the Lyapunov spectrum of an expanding map need not be concave, and posed various problems concerning the possible number of inflection points. In this paper we answer a conjecture in Iommi and Kiwi (2009) by proving that the Lyapunov spectrum of a two branch piecewise linear map has at most two points of inflection. We then answer a question in Iommi and Kiwi (2009) by proving that there exist finite branch piecewise linear maps whose Lyapunov spectra have arbitrarily many points of inflection. This approach is used to exhibit a countable branch piecewise linear map whose Lyapunov spectrum has infinitely many points of inflection.
Item Type: | Journal Article | |||||||||
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Subjects: | Q Science > QA Mathematics Q Science > QC Physics |
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Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | |||||||||
SWORD Depositor: | Library Publications Router | |||||||||
Library of Congress Subject Headings (LCSH): | Lyapunov functions , Mathematical physics, Dimension theory (Topology) | |||||||||
Journal or Publication Title: | Communications in Mathematical Physics | |||||||||
Publisher: | Springer | |||||||||
ISSN: | 0010-3616 | |||||||||
Official Date: | 26 July 2021 | |||||||||
Dates: |
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Volume: | 386 | |||||||||
Number: | 3 | |||||||||
Page Range: | pp. 1383-1411 | |||||||||
DOI: | 10.1007/s00220-021-04161-4 | |||||||||
Status: | Peer Reviewed | |||||||||
Publication Status: | Published | |||||||||
Access rights to Published version: | Open Access (Creative Commons) | |||||||||
Date of first compliant deposit: | 17 January 2022 | |||||||||
Date of first compliant Open Access: | 18 January 2022 | |||||||||
RIOXX Funder/Project Grant: |
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