Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Invariant densities and escape rates: Rigorous and computable
  approximations in the $L^{\infty}$-norm   In this article we study a piecewise linear discretization schemes for
transfer operators (Perron-Frobenius operators) associated with interval maps.
We show how these can be used to provide rigorous {\bf pointwise}
approximations for invariant densities of Markov interval maps. We also derive
the order of convergence of the approximate invariant density to the real one
in the $L^{\infty}$-norm. The outcome of this paper complements rigorous
results on $L^1$ approximations of invariant densities \cite{KMY} and recent
results on the formulae of escape rates of open dynamical systems \cite{KL2}.
We implement our computations on two examples (one rigorous and one
non-rigorous) to illustrate the feasibility and efficiency of our schemes.

23
The categories of this paper are: solv-int
17
The categories of this paper are: q-fin
8
The categories of this paper are: hep-ex
18
The categories of this paper are: econ
26
The categories of this paper are: bayes-an
22
The categories of this paper are: chao-dyn
37
The categories of this paper are: supr-con
31
The categories of this paper are: ao-sci
5
The categories of this paper are: gr-qc
15
The categories of this paper are: nucl-ex
10
The categories of this paper are: q-bio
27
The categories of this paper are: comp-gas
21
The categories of this paper are: adap-org
29
The categories of this paper are: funct-an
35
The categories of this paper are: mtrl-th
34
The categories of this paper are: chem-ph