Dynamical systems and categories
Abstract
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.
Cite
@article{arxiv.1307.8418,
title = {Dynamical systems and categories},
author = {George Dimitrov and Fabian Haiden and Ludmil Katzarkov and Maxim Kontsevich},
journal= {arXiv preprint arXiv:1307.8418},
year = {2022}
}
Comments
35 pages