Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Sensitivity of steady states in a degenerately-damped stochastic Lorenz
  system   We study stability of solutions for a randomly driven and degenerately damped
version of the Lorenz '63 model. Specifically, we prove that when damping is
absent in one of the temperature components, the system possesses a unique
invariant probability measure if and only if noise acts on the convection
variable. On the other hand, if there is a positive growth term on the vertical
temperature profile, we prove that there is no normalizable invariant state.
Our approach relies on the derivation and analysis of non-trivial Lyapunov
functions which ensure positive recurrence or null-recurrence/transience of the
dynamics.

3
The categories of this paper are: physics
22
The categories of this paper are: chao-dyn
20
The categories of this paper are: acc-phys
0
The categories of this paper are: hep-ph
29
The categories of this paper are: funct-an
19
The categories of this paper are: eess
31
The categories of this paper are: ao-sci
5
The categories of this paper are: gr-qc
35
The categories of this paper are: mtrl-th
13
The categories of this paper are: quant-ph
26
The categories of this paper are: bayes-an
33
The categories of this paper are: plasm-ph
36
The categories of this paper are: cmp-lg
9
The categories of this paper are: nlin
1
The categories of this paper are: cs
16
The categories of this paper are: stat