Dynamical systems and categories

By George Dimitrov, F. Haiden, L. Katzarkov, M. Kontsevich. 2013

104 citations recorded by the source corpus.

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.

Subfields: Discrete Mathematics and Combinatorics, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/33f7744c3994a26941fdb790c37eb6d0d498df50

Citations in the corpus

• Flat surfaces and stability structures (2014, unknown): “nd, the t-structures are not nite length. Closely related is the question of the distribution of phases of stable objects, in particular density, which was investigated by Dimitrov and the authors in [14]. 1.4 Meromorphic connections on T C and Nevanlinna’s Kernpolygon For a meromorphic quadratic di”