Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the dynamical and arithmetic degrees of rational self-maps of
  algebraic varieties   Let f : X --> X be a dominant rational map of a projective variety defined
over a global field, let d_f be the dynamical degree of f, and let h_X be a
Weil height on X relative to an ample divisor. We prove that h_X(f^n(P)) <<
(d_f + e)^n h_X(P), where the implied constant depends only on X, h_X, f, and
e. As applications, we prove a fundamental inequality a_f(P) \le d_f for the
upper arithmetic degree and we construct canonical heights for (nef) divisors.
We conjecture that a_f(P) = d_f whenever the orbit of P is Zariski dense, and
we describe some cases for which we can prove our conjecture.

24
The categories of this paper are: dg-ga
18
The categories of this paper are: econ
29
The categories of this paper are: funct-an
0
The categories of this paper are: hep-ph
13
The categories of this paper are: quant-ph
5
The categories of this paper are: gr-qc
31
The categories of this paper are: ao-sci
17
The categories of this paper are: q-fin
14
The categories of this paper are: math-ph
4
The categories of this paper are: cond-mat
22
The categories of this paper are: chao-dyn
12
The categories of this paper are: nucl-th
26
The categories of this paper are: bayes-an
9
The categories of this paper are: nlin
6
The categories of this paper are: astro-ph
23
The categories of this paper are: solv-int