Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Sub-Finsler geodesics on the Cartan group   This paper is a continuation of the work by the same authors on the Cartan
group equipped with the sub-Finsler $\ell_\infty$ norm. We start by giving a
detailed presentation of the structure of bang-bang extremal trajectories. Then
we prove upper bounds on the number of switchings on bang-bang minimizers. We
prove that any normal extremal is either bang-bang, or singular, or mixed.
Consequently, we study mixed extremals. In particular, we prove that every two
points can be connected by a piecewise smooth minimizer, and we give a uniform
bound on the number of such pieces.

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The categories of this paper are: nlin
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The categories of this paper are: comp-gas
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The categories of this paper are: mtrl-th
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The categories of this paper are: dg-ga
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The categories of this paper are: ao-sci
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The categories of this paper are: nucl-ex
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The categories of this paper are: q-fin
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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: math-ph
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The categories of this paper are: eess
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The categories of this paper are: adap-org
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The categories of this paper are: acc-phys
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The categories of this paper are: hep-ex
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The categories of this paper are: q-alg
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The categories of this paper are: cmp-lg