Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Dimension estimates for $C^1$ iterated function systems and repellers.
  Part I   This is the first article in a two-part series containing some results on
dimension estimates for $C^1$ iterated function systems and repellers. In this
part, we prove that the upper box-counting dimension of the attractor of any
$C^1$ iterated function system (IFS) on ${\Bbb R}^d$ is bounded above by its
singularity dimension, and the upper packing dimension of any ergodic invariant
measure associated with this IFS is bounded above by its Lyapunov dimension.
Similar results are obtained for the repellers for $C^1$ expanding maps on
Riemannian manifolds.

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The categories of this paper are: astro-ph
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The categories of this paper are: nucl-ex
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The categories of this paper are: adap-org
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The categories of this paper are: bayes-an
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The categories of this paper are: alg-geom
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The categories of this paper are: nlin
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The categories of this paper are: cond-mat
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The categories of this paper are: nucl-th
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The categories of this paper are: hep-ex
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The categories of this paper are: supr-con
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The categories of this paper are: patt-sol
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The categories of this paper are: plasm-ph
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The categories of this paper are: dg-ga
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The categories of this paper are: q-bio
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The categories of this paper are: q-alg
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The categories of this paper are: math-ph