For classical dynamical systems, the polynomial entropy serves as a refined invariant of the
topological entropy. In the setting of categorical dynamical systems, that is, triangulated …

In this paper, we construct a compactification of the space of Bridgeland stability conditions
on a smooth projective curve, as an analogue of Thurston compactifications in Teichm\" uller …

On a Weierstraß elliptic surface, we describe the action of the relative Fourier-Mukai
transform on the geometric chamber of Stab (X), and in the K3 case we also study the action …

We study invariants, called shifting numbers, that measure the asymptotic amount by which
an autoequivalence of a triangulated category translates inside the category. The invariants …

We propose compactifications of the moduli space of Bridgeland stability conditions of a
triangulated category. Our construction arises from a viewing a stability condition as a metric …

Recent developments in the theory of stability conditions and its relation to Teichmuller
theory have revealed a deep connection between triangulated categories and surfaces …

In this paper, being motivated by symplectic topology, we study categorical entropy.
Specifically, we prove inequalities between categorical entropies of functors on a category …

Abstract We consider a 3-Calabi–Yau triangulated category associated to an ideal
triangulation of a marked bordered surface. Using the theory of harmonic maps between …

Given a triangulated category $\mathcal {C} $, we construct a partial compactification,
denoted $\mathcal {A}\mathrm {Stab}(\mathcal {C}) $, of the quotient of its stability manifold …

In topological dynamics, the Gromov–Yomdin theorem states that the topological entropy of
a holomorphic automorphism f of a smooth projective variety is equal to the logarithm of the …