Dynamical systems and categories
Dynamical systems and categories
复制标题
动力系统和类别
DOI：
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发表时间：
2013
期刊：
影响因子：
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通讯作者：
M. Kontsevich
中科院分区：
文献类型：
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作者：
G. Dimitrov;F. Haiden;L. Katzarkov;M. Kontsevich
我们研究的动力系统的经典理论中的三角和A-无穷大范畴的背景下的结果的动机问题。首先，熵被定义为精确的内函子，并在各种例子中计算。特别地，从福谷范畴上的诱导函子恢复了伪Anosov映射的经典熵。其次，研究了Bridgeland稳定性条件的相集的稠密性，并在有界导范畴的情况下给出了一个完整的答案。三角范畴中的某些例外对，我们称之为克罗内克对，被用来构造具有相密度的稳定性条件。一些开放的问题和进一步的方向，以及概述。
We study questions motivated by results in the classical theory of dynamical systems in the context of triangulated and A-infinity categories. First, entropy is defined for exact endofunctors and computed in a variety of examples. In particular, the classical entropy of a pseudo-Anosov map is recovered from the induced functor on the Fukaya category. Second, the density of the set of phases of a Bridgeland stability condition is studied and a complete answer is given in the case of bounded derived categories of quivers. Certain exceptional pairs in triangulated categories, which we call Kronecker pairs, are used to construct stability conditions with density of phases. Some open questions and further directions are outlined as well.
影响因子：
6.2
作者：
Bridgeland, Tom;Smith, Ivan
通讯作者：
Smith, Ivan