Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Entropy and periodic orbits for equivalent smooth flows   Given any $K>0$, we construct two equivalent $C^2$ flows, one of which has
positive topological entropy larger than $K$ and admits zero as the exponential
growth of periodic orbits, in contrast, the other has zero topological entropy
and super-exponential growth of periodic orbits. Moreover we establish a
$C^{\infty}$ flow on $\mathbb{S}^2$ with super-exponential growth of periodic
orbits, which is also equivalent to another flow with zero exponential growth
of periodic orbits. On the other hand, any two dimensional flow has only zero
topological entropy.

3
The categories of this paper are: physics
30
The categories of this paper are: q-alg
19
The categories of this paper are: eess
31
The categories of this paper are: ao-sci
16
The categories of this paper are: stat
4
The categories of this paper are: cond-mat
11
The categories of this paper are: hep-lat
7
The categories of this paper are: hep-th
1
The categories of this paper are: cs
10
The categories of this paper are: q-bio
23
The categories of this paper are: solv-int
32
The categories of this paper are: atom-ph
22
The categories of this paper are: chao-dyn
27
The categories of this paper are: comp-gas
5
The categories of this paper are: gr-qc
20
The categories of this paper are: acc-phys