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How Many Inflections are There in the Lyapunov Spectrum?
- Source :
-
Communications in Mathematical Physics . Sep2021, Vol. 386 Issue 3, p1383-1411. 29p. - Publication Year :
- 2021
-
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. [ABSTRACT FROM AUTHOR]
- Subjects :
- *LINEAR operators
*INFLECTION (Grammar)
Subjects
Details
- Language :
- English
- ISSN :
- 00103616
- Volume :
- 386
- Issue :
- 3
- Database :
- Academic Search Index
- Journal :
- Communications in Mathematical Physics
- Publication Type :
- Academic Journal
- Accession number :
- 151881013
- Full Text :
- https://doi.org/10.1007/s00220-021-04161-4