Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: $W$-like maps with various instabilities of acim's   This paper generalizes the results of [13] and then provides an interesting
example. We construct a family of $W$-like maps $\{W_a\}$ with a turning fixed
point having slope $s_1$ on one side and $-s_2$ on the other. Each $W_a$ has an
absolutely continuous invariant measure $\mu_a$. Depending on whether
$\frac{1}{s_1}+\frac{1}{s_2}$ is larger, equal or smaller than 1, we show that
the limit of $\mu_a$ is a singular measure, a combination of singular and
absolutely continuous measure or an absolutely continuous measure,
respectively. It is known that the invariant density of a single piecewise
expanding map has a positive lower bound on its support. In Section 4 we give
an example showing that in general, for a family of piecewise expanding maps
with slopes larger than 2 in modulus and converging to a piecewise expanding
map, their invariant densities do not necessarily have a positive lower bound
on the support.

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The categories of this paper are: bayes-an
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The categories of this paper are: q-fin
12
The categories of this paper are: nucl-th
13
The categories of this paper are: quant-ph
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The categories of this paper are: funct-an
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The categories of this paper are: stat
14
The categories of this paper are: math-ph
6
The categories of this paper are: astro-ph
35
The categories of this paper are: mtrl-th
8
The categories of this paper are: hep-ex
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The categories of this paper are: nucl-ex
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The categories of this paper are: ao-sci
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The categories of this paper are: cmp-lg
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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: acc-phys