On pseudo-Anosov autoequivalences

Motivated by results of Thurston, we prove that any autoequivalence of a
triangulated category induces a filtration by triangulated subcategories, provided the existence of Bridgeland stability conditions. The filtration is given by the exponential growth
rate of masses under iterates of the autoequivalence, and only depends on the choice
of a connected component of the stability manifold. We then propose a new definition
of pseudo-Anosov autoequivalences, and prove that our definition is more general than
the one previously proposed by Dimitrov, Haiden, Katzarkov, and Kontsevich. We construct new examples of pseudo-Anosov autoequivalences on the derived categories of quintic
Calabi–Yau threefolds and quiver Calabi–Yau categories. Finally, we prove that certain
pseudo-Anosov autoequivalences on quiver 3-Calabi–Yau categories act hyperbolically on
the space of Bridgeland stability conditions.