Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Badly approximable points on planar curves and a problem of Davenport   Let C be two times continuously differentiable curve in R^2 with at least one
point at which the curvature is non-zero. For any i,j > 0 with i+j =1, let
Bad(i,j) denote the set of points (x,y) in R^2 for which max {||qx ||^{1/i},
||qy||^{1/j}} > c/q for all integers q >0. Here c = c(x,y) is a positive
constant. Our main result implies that any finite intersection of such sets
with C has full Hausdorff dimension. This provides a solution to a problem of
Davenport dating back to the sixties.

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The categories of this paper are: chao-dyn
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The categories of this paper are: chem-ph
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The categories of this paper are: nlin
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The categories of this paper are: nucl-th
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The categories of this paper are: eess
3
The categories of this paper are: physics
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The categories of this paper are: hep-ex
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The categories of this paper are: gr-qc
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The categories of this paper are: econ
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The categories of this paper are: bayes-an
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The categories of this paper are: mtrl-th
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The categories of this paper are: ao-sci
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The categories of this paper are: q-fin
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The categories of this paper are: hep-th
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The categories of this paper are: math-ph
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The categories of this paper are: adap-org