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.

35 pages

References in corpus (1)

• Wild Wall Crossing and BPS Giants

Cited by in corpus (9)

• On entropy for autoequivalences of the derived category of curves
• Categorical polynomial entropy
• Curvature of the space of stability conditions
• Serre dimension and stability conditions
• Hochschild entropy and Categorical entropy
• A comparison of categorical and topological entropies on Weinstein manifolds
• Symplectomorphisms and spherical objects in the conifold smoothing
• Algebraic invariants of orbit configuration spaces in genus zero associated to finite groups
• Heisenberg homology on surface configurations