Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: An abstract continuity theorem of the Lyapunov exponents   We devise an abstract, modular scheme to prove continuity of the Lyapunov
exponents for a general class of linear cocycles. The main assumption is the
availability of appropriate large deviation type (LDT) estimates which are
uniform in the data. We provide a modulus of continuity that depends explicitly
on the sharpness of the LDT estimate. Our method uses an inductive procedure
based on the deterministic, general Avalanche Principle in [4]. The main
advantage of this approach, besides the fact that it provides quantitative
estimates, is its versatility, as it applies to quasi-periodic cocycles (one
and multivariable torus translations), to random cocycles (i.i.d. and Markov
systems) and to any other types of base dynamics as long as appropriate LDT
estimates are satisfied. Moreover, compared to other available quantitative
results for quasi-periodic or random cocycles, this method allows for weaker
assumptions.
  This is a draft of a chapter in our forthcoming research monograph [4].

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The categories of this paper are: hep-ph
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The categories of this paper are: hep-lat
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The categories of this paper are: dg-ga
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The categories of this paper are: nucl-th
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The categories of this paper are: q-fin
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The categories of this paper are: adap-org
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The categories of this paper are: physics
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The categories of this paper are: supr-con
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The categories of this paper are: q-bio
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The categories of this paper are: acc-phys
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The categories of this paper are: hep-th
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The categories of this paper are: gr-qc
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The categories of this paper are: solv-int
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The categories of this paper are: hep-ex
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The categories of this paper are: cmp-lg
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The categories of this paper are: mtrl-th