Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Bifurcations and Transitions to Chaos in An Inverted Pendulum   We consider a parametrically forced pendulum with a vertically oscillating
suspension point. It is well known that, as the amplitude of the vertical
oscillation is increased, its inverted state (corresponding to the
vertically-up configuration) undergoes a cascade of ``resurrections,'' i.e., it
becomes stabilized after its instability, destabilize again, and so forth ad
infinitum. We make a detailed numerical investigation of the bifurcations
associated with such resurrections of the inverted pendulum by varying the
amplitude and frequency of the vertical oscillation. It is found that the
inverted state stabilizes via alternating ``reverse'' subcritical pitchfork and
period-doubling bifurcations, while it destabilizes via alternating ``normal''
supercritical period-doubling and pitchfork bifrucations. An infinite sequence
of period-doubling bifurcations, leading to chaos, follows each destabilization
of the inverted state. The critical behaviors in the period-doubling cascades
are also discussed.

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The categories of this paper are: mtrl-th
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The categories of this paper are: funct-an
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The categories of this paper are: supr-con
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The categories of this paper are: physics
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The categories of this paper are: alg-geom
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The categories of this paper are: quant-ph
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The categories of this paper are: nucl-th
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The categories of this paper are: solv-int
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The categories of this paper are: math
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The categories of this paper are: acc-phys
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The categories of this paper are: hep-ph
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The categories of this paper are: dg-ga
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The categories of this paper are: adap-org
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The categories of this paper are: gr-qc
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The categories of this paper are: bayes-an
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The categories of this paper are: chem-ph