Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The doubling map with asymmetrical holes   Let $0<a<b<1$ and let $T$ be the doubling map. Set $\mathcal
J(a,b):=\{x\in[0,1] : T^nx\notin (a,b), n\ge0\}$. In this paper we completely
characterize the holes $(a,b)$ for which any of the following scenarios holds:
{enumerate} $\mathcal J(a,b)$ contains a point $x\in(0,1)$; $\mathcal
J(a,b)\cap [\de,1-\de]$ is infinite for any fixed $\de>0$; $\mathcal J(a,b)$ is
uncountable of zero Hausdorff dimension; $\mathcal J(a,b)$ is of positive
Hausdorff dimension. {enumerate} In particular, we show that (iv) is always the
case if \[ b-a<\frac14\prod_{n=1}^\infty \bigl(1-2^{-2^n}\bigr)\approx 0.175092
\] and that this bound is sharp. As a corollary, we give a full description of
first and second order critical holes introduced in \cite{SSC} for the doubling
map.
  Furthermore, we show that our model yields a continuum of "routes to chaos"
via arbitrary sequences of products of natural numbers, thus generalizing the
standard route to chaos via period doubling.

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The categories of this paper are: hep-lat
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The categories of this paper are: mtrl-th
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The categories of this paper are: plasm-ph
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The categories of this paper are: funct-an
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The categories of this paper are: stat
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The categories of this paper are: supr-con
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The categories of this paper are: astro-ph
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The categories of this paper are: math-ph
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The categories of this paper are: chao-dyn
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The categories of this paper are: solv-int
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The categories of this paper are: q-fin
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The categories of this paper are: nlin
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The categories of this paper are: gr-qc
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The categories of this paper are: alg-geom
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The categories of this paper are: bayes-an
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The categories of this paper are: patt-sol