Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Separation of trajectories and its Relation to Entropy for Intermittent
  Systems with a Zero Lyapunov exponent   One dimensional intermittent maps with stretched exponential separation of
nearby trajectories are considered. When time goes infinity the standard
Lyapunov exponent is zero. We investigate the distribution of
$\lambda_{\alpha}= \sum_{i=0}^{t-1} \ln \left| M'(x_i) \right|/t^{\alpha}$,
where $\alpha$ is determined by the nonlinearity of the map in the vicinity of
marginally unstable fixed points. The mean of $\lambda_{\alpha}$ is determined
by the infinite invariant density. Using semi analytical arguments we calculate
the infinite invariant density for the Pomeau-Manneville map, and with it
obtain excellent agreement between numerical simulation and theory. We show
that $\alpha \left< \lambda_{\alpha}\right>$ is equal to Krengel's entropy and
to the complexity calculated by the Lempel-Ziv compression algorithm. This
generalized Pesin's identity shows that $\left< \lambda_{\alpha}\right>$ and
Krengel's entropy are the natural generalizations of usual Lyapunov exponent
and entropy for these systems.

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The categories of this paper are: q-bio
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The categories of this paper are: mtrl-th
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The categories of this paper are: gr-qc
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The categories of this paper are: math
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The categories of this paper are: physics
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The categories of this paper are: atom-ph
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The categories of this paper are: chem-ph
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The categories of this paper are: acc-phys
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The categories of this paper are: eess
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The categories of this paper are: quant-ph
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The categories of this paper are: math-ph
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The categories of this paper are: hep-th
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The categories of this paper are: bayes-an
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The categories of this paper are: econ
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The categories of this paper are: cs
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The categories of this paper are: dg-ga