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A NOTE ON ENTROPY OF AUTO-EQUIVALENCES: LOWER BOUND AND THE CASE OF ORBIFOLD PROJECTIVE LINES

Published online by Cambridge University Press:  26 June 2018

KOHEI KIKUTA
Affiliation:
Department of Mathematics, Graduate School of Science, Osaka University, Toyonaka, Osaka, 560-0043, Japan email [email protected]
YUUKI SHIRAISHI
Affiliation:
International college, Osaka University, Toyonaka, Osaka, 560-0043, Japan email [email protected]
ATSUSHI TAKAHASHI
Affiliation:
Department of Mathematics, Graduate School of Science, Osaka University, Toyonaka, Osaka, 560-0043, Japan email [email protected]

Abstract

Entropy of categorical dynamics is defined by Dimitrov–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.

Type
Article
Copyright
© 2018 Foundation Nagoya Mathematical Journal

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