A note on entropy of auto-equivalences: lower bound and the case of orbifold projective lines

Abstract

Entropy of categorical dynamics is defined by Dmitrov-Haiden-Katzarkov-Kontsevich. Motivated by the fundamental theorem of the topological entropy due to Gromov-Yomdin, it is natural to ask an equality between the entropy and the spectral radius of induced morphisms on the numerical Grothendieck group. In this paper, we add two results on this equality: the lower bound in a general setting and the equality for orbifold projective lines.

15 pages. v2: minor changes

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Cited by in corpus (13)

• Categorical polynomial entropy
• On the categorical entropy and the topological entropy
• Categorical vs topological entropy of autoequivalences of surfaces
• Asymptotic shifting numbers in triangulated categories
• Entropy of an autoequivalence on Calabi-Yau manifolds
• Entropy of the composition of two spherical twists
• On entropy of spherical twists
• Hochschild entropy and Categorical entropy
• On Gromov-Yomdin type theorems and a categorical interpretation of holomorphicity
• Spherical twists and the center of autoequivalence groups of K3 surfaces
• Spherical twists, relations and the center of autoequivalence groups of K3 surfaces
• Categorical dynamical systems arising from sign-stable mutation loops
• Entropy of monomial algebras and derived categories