Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Stability by linear approximation for time scale dynamical systems   We study systems on time scales that are generalizations of classical
differential or difference equations. In this paper we consider linear systems
and their small nonlinear perturbations. In terms of time scales and of
eigenvalues of matrices we formulate conditions, sufficient for stability by
linear approximation. We demonstrate that those conditions are close to
necessary ones. For non-periodic time scales we use techniques of central upper
Lyapunov exponents (a common tool of the theory of linear ODEs) to study
stability of solutions. Also, time scale versions of the famous Chetaev's
theorem on conditional instability are proved.

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The categories of this paper are: supr-con
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The categories of this paper are: patt-sol
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The categories of this paper are: cmp-lg
10
The categories of this paper are: q-bio
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The categories of this paper are: nucl-th
18
The categories of this paper are: econ
17
The categories of this paper are: q-fin
21
The categories of this paper are: adap-org
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The categories of this paper are: q-alg
20
The categories of this paper are: acc-phys
16
The categories of this paper are: stat
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The categories of this paper are: chem-ph
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The categories of this paper are: nucl-ex
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The categories of this paper are: astro-ph
31
The categories of this paper are: ao-sci
14
The categories of this paper are: math-ph