Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A functional analytic approach to perturbations of the Lorentz gas   We present a functional analytic framework based on the spectrum of the
transfer operator to study billiard maps associated with perturbations of the
periodic Lorentz gas. We show that recently constructed Banach spaces for the
billiard map of the classical Lorentz gas are flexible enough to admit a wide
variety of perturbations, including: movements and deformations of scatterers;
billiards subject to external forces; nonelastic reflections with kicks and
slips at the boundaries of the scatterers; and random perturbations comprised
of these and possibly other classes of maps. The spectra and spectral
projections of the transfer operators are shown to vary continuously with such
perturbations so that the spectral gap enjoyed by the classical billiard
persists and important limit theorems follow.

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The categories of this paper are: solv-int
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The categories of this paper are: nlin
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The categories of this paper are: stat
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The categories of this paper are: alg-geom
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The categories of this paper are: gr-qc
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The categories of this paper are: nucl-ex
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The categories of this paper are: quant-ph
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The categories of this paper are: acc-phys
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The categories of this paper are: nucl-th
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The categories of this paper are: dg-ga
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The categories of this paper are: hep-th
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The categories of this paper are: math-ph
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The categories of this paper are: supr-con
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The categories of this paper are: bayes-an
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The categories of this paper are: chao-dyn
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The categories of this paper are: econ