Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Ermakov Systems with Multiplicative Noise   Using the Euler-Maruyama numerical method, we present calculations of the
Ermakov-Lewis invariant and the dynamic, geometric, and total phases for
several cases of stochastic parametric oscillators, including the simplest case
of the stochastic harmonic oscillator. The results are compared with the
corresponding numerical noiseless cases to evaluate the effect of the noise.
Besides, the noiseless cases are analytic and their analytic solutions are
briefly presented. The Ermakov-Lewis invariant is not affected by the
multiplicative noise in the three particular examples presented in this work,
whereas there is a shift effect in the case of the phases

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The categories of this paper are: math-ph
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The categories of this paper are: hep-ex
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The categories of this paper are: ao-sci
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The categories of this paper are: nucl-th
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The categories of this paper are: physics
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The categories of this paper are: gr-qc
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The categories of this paper are: hep-lat
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The categories of this paper are: nucl-ex
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The categories of this paper are: chem-ph
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The categories of this paper are: dg-ga
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The categories of this paper are: astro-ph
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The categories of this paper are: solv-int
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The categories of this paper are: acc-phys
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The categories of this paper are: cmp-lg
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The categories of this paper are: funct-an
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The categories of this paper are: stat