Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Abundance of observable Lyapunov irregular sets   Lyapunov exponent is widely used in natural science to find chaotic signal,
but its existence is seldom discussed. In the present paper, we consider the
problem of whether the set of points at which Lyapunov exponent fails to exist,
called the Lyapunov irregular set, has positive Lebesgue measure. The only
known example with the Lyapunov irregular set of positive Lebesgue measure is a
figure-8 attractor by the work of Ott and Yorke [OY2008], whose key mechanism
(homoclinic loop) is easy to be broken by small perturbations. In this paper,
we show that surface diffeomorphisms with a robust homoclinic tangency given by
Colli and Vargas [CV2001], as well as other several known nonhyperbolic
dynamics, has the Lyapunov irregular set of positive Lebesgue measure. We can
construct such positive Lebesgue measure sets both as the time averages exist
and do not exist on it.

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The categories of this paper are: chem-ph
5
The categories of this paper are: gr-qc
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The categories of this paper are: q-fin
0
The categories of this paper are: hep-ph
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The categories of this paper are: supr-con
24
The categories of this paper are: dg-ga
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The categories of this paper are: patt-sol
3
The categories of this paper are: physics
26
The categories of this paper are: bayes-an
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The categories of this paper are: funct-an
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The categories of this paper are: econ
10
The categories of this paper are: q-bio
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The categories of this paper are: ao-sci
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The categories of this paper are: plasm-ph
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The categories of this paper are: hep-lat
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The categories of this paper are: quant-ph