How Many Inflections are There in the Lyapunov Spectrum?
How Many Inflections are There in the Lyapunov Spectrum?
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DOI：
10.1007/s00220-021-04161-4
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发表时间：
2020-02
影响因子：
2.4
通讯作者：
O. Jenkinson;M. Pollicott;P. Vytnova
中科院分区：
文献类型：
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作者：
O. Jenkinson;M. Pollicott;P. Vytnova
Iommi和Kiwi （J Stat Phys 135:535-546, 2009）证明了扩展图的Lyapunov谱不一定是凹的，并提出了关于拐点可能数量的各种问题。本文通过证明两个分支分段线性映射的Lyapunov谱最多有两个拐点来回答Iommi和Kiwi（2009）中的一个猜想。然后，我们回答了Iommi和Kiwi（2009）中的一个问题，证明存在有限分支分段线性映射，其Lyapunov谱具有任意多个拐点。用这种方法展示了一个李雅普诺夫谱具有无穷多个拐点的可数分支分段线性映射。
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.