论文标题
Lyapunov频谱中有多少个弯曲？
How many inflections are there in the Lyapunov spectrum?
论文作者
论文摘要
Iommi＆Kiwi表明，扩展地图的Lyapunov光谱不必凹入，并且在可能的拐点数量上提出了各种问题。在本文中，我们通过证明了两个分支分段线性图的Lyapunov频谱最多具有两个分配点，从而回答了Iommi＆Kiwi的猜想。然后，我们通过证明存在有限分支分段线性地图来回答Iommi＆Kiwi的问题，其Lyapunov Spectra是任意拐点的多点。这种方法用于展示可数的分支分段线性图，其Lyapunov光谱具有无限的拐点。
Iommi & Kiwi 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 of Iommi & Kiwi 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 of Iommi & Kiwi 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.
