Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: q-damped Oscillator and degenerate roots of constant coefficients
  q-difference ODE   The classical model of q-damped oscillator is introduced and solved in terms
of Jackson q-exponential function for three different cases, under-damped,
over-damped and the critical one. It is shown that in all three cases solution
is oscillating in time but is unbounded and non-periodic. By q-periodic
function modulation, the self-similar micro-structure of the solution for small
time intervals is derived. In the critical case with degenerate roots, the
second linearly independent solution is obtained as a limiting case of two
infinitesimally close roots. It appears as standard derivative of q-exponential
and is rewritten in terms of the q-logarithmic function. We extend our result
by constructing n linearly independent set of solutions to a generic constant
coefficient q-difference equation degree N with n degenerate roots.

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The categories of this paper are: eess
15
The categories of this paper are: nucl-ex
30
The categories of this paper are: q-alg
7
The categories of this paper are: hep-th
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The categories of this paper are: econ
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The categories of this paper are: q-fin
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The categories of this paper are: patt-sol
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The categories of this paper are: atom-ph
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The categories of this paper are: stat
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The categories of this paper are: solv-int
3
The categories of this paper are: physics
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The categories of this paper are: bayes-an
4
The categories of this paper are: cond-mat
1
The categories of this paper are: cs
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The categories of this paper are: hep-lat
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The categories of this paper are: chem-ph