A NOTE ON ENTROPY OF AUTO-EQUIVALENCES: LOWER BOUND AND THE CASE OF ORBIFOLD PROJECTIVE LINES
A NOTE ON ENTROPY OF AUTO-EQUIVALENCES: LOWER BOUND AND THE CASE OF ORBIFOLD PROJECTIVE LINES
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关于自等价熵的注记：下界和 Orbifold 投影线的情况
DOI：
10.1017/nmj.2018.21
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发表时间：
2018
影响因子：
0.8
通讯作者：
TAKAHASHI ATSUSHI
中科院分区：
文献类型：
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作者：
KIKUTA KOHEI;SHIRAISHI YUUKI;TAKAHASHI ATSUSHI
范畴动力学的熵由迪米特罗夫-海登-卡扎尔科夫-康采维奇定义。在Gromov-Yomdin拓扑熵基本定理的启发下，很自然地要求数值Grothendieck群上诱导态射的熵与谱半径相等。在这篇文章中，我们增加了两个关于这个等式的结果：一般情况下的下界和奥分叶投影线的等式。
Entropy of categorical dynamics is defined by Dimitrov–Haiden–Katzarkov–Kontsevich. Motivated by the fundamental theorem of the topological entropy due to Gromov–Yomdin, it is natural to ask an equality between the entropy and the spectral radius of induced morphisms on the numerical Grothendieck group. In this paper, we add two results on this equality: the lower bound in a general setting and the equality for orbifold projective lines.