Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Complexity of Ten Decision Problems in Continuous Time Dynamical Systems   We show that for continuous time dynamical systems described by polynomial
differential equations of modest degree (typically equal to three), the
following decision problems which arise in numerous areas of systems and
control theory cannot have a polynomial time (or even pseudo-polynomial time)
algorithm unless P=NP: local attractivity of an equilibrium point, stability of
an equilibrium point in the sense of Lyapunov, boundedness of trajectories,
convergence of all trajectories in a ball to a given equilibrium point,
existence of a quadratic Lyapunov function, invariance of a ball, invariance of
a quartic semialgebraic set under linear dynamics, local collision avoidance,
and existence of a stabilizing control law. We also extend our earlier
NP-hardness proof of testing local asymptotic stability for polynomial vector
fields to the case of trigonometric differential equations of degree four.

8
The categories of this paper are: hep-ex
27
The categories of this paper are: comp-gas
0
The categories of this paper are: hep-ph
34
The categories of this paper are: chem-ph
5
The categories of this paper are: gr-qc
26
The categories of this paper are: bayes-an
32
The categories of this paper are: atom-ph
23
The categories of this paper are: solv-int
19
The categories of this paper are: eess
15
The categories of this paper are: nucl-ex
25
The categories of this paper are: patt-sol
29
The categories of this paper are: funct-an
9
The categories of this paper are: nlin
36
The categories of this paper are: cmp-lg
37
The categories of this paper are: supr-con
33
The categories of this paper are: plasm-ph