Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On entropy for autoequivalences of the derived category of curves   To an exact endofunctor of a triangulated category with a split-generator,
the notion of entropy is given by Dimitrov-Haiden-Katzarkov-Kontsevich, which
is a (possibly negative infinite) real-valued function of a real variable. It
is important to evaluate the value of the entropy at zero in relation to the
topological entropy. In this paper, we study the entropy at zero of an exact
autoequivalence of the derived category of a complex smooth projective curve,
and prove that it coincides with the natural logarithm of the spectral radius
of the induced automorphism on its numerical Grothendieck group.

34
The categories of this paper are: chem-ph
25
The categories of this paper are: patt-sol
10
The categories of this paper are: q-bio
4
The categories of this paper are: cond-mat
12
The categories of this paper are: nucl-th
31
The categories of this paper are: ao-sci
29
The categories of this paper are: funct-an
36
The categories of this paper are: cmp-lg
16
The categories of this paper are: stat
9
The categories of this paper are: nlin
27
The categories of this paper are: comp-gas
23
The categories of this paper are: solv-int
21
The categories of this paper are: adap-org
13
The categories of this paper are: quant-ph
7
The categories of this paper are: hep-th
37
The categories of this paper are: supr-con