Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Summable Orbits   We introduce a class of orbits which may have $0$ Lyapunov exponents, but
still demonstrate some sensitivity to initial conditions. We construct a
countable Markov partition with a finite-to-one almost everywhere induced
coding, and which lifts the geometric potential with summable variations (for a
$C^{1+}$ diffeomorphism of a closed manifold of dimension $\geq2$). An
important tool we use is a shadowing theory for orbits which may have $0$
Lyapunov exponents.
  We construct (weak) stable and unstable leaves for such orbits using a Graph
Transform method, and prove the absolute continuity of these foliations w.r.t
holonomies. In particular, we discuss setups where these foliations exist, and
are strictly weak -- i.e., do not demonstrate exponential contraction. One
example is a family of non-uniformly hyperbolic diffeomorhpims where we are
able to simultaneously code all invariant measures in a finite-to-one almost
everyhwere fashion.

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The categories of this paper are: hep-lat
9
The categories of this paper are: nlin
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The categories of this paper are: math-ph
28
The categories of this paper are: alg-geom
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The categories of this paper are: quant-ph
21
The categories of this paper are: adap-org
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The categories of this paper are: hep-th
35
The categories of this paper are: mtrl-th
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The categories of this paper are: supr-con
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The categories of this paper are: chao-dyn
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The categories of this paper are: astro-ph
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The categories of this paper are: gr-qc
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The categories of this paper are: q-fin
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The categories of this paper are: q-bio
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The categories of this paper are: eess
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The categories of this paper are: solv-int