Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On new fractal phenomena connected with infinite linear IFS   We establish several new fractal and number theoretical phenomena connected
with expansions which are generated by infinite linear iterated function
systems. First of all we show that the systems $\Phi$ of cylinders of
generalized L\"uroth expansions are, generally speaking, not faithful for the
Hausdorff dimension calculation. Using Yuval Peres' approach, we prove
sufficient conditions for the non-faithfulness of such families of cylinders.
  On the other hand, rather general sufficient conditions for the faithfulness
of such covering systems are also found. As a corollary of our main results, we
obtain the non-faithfullness of the family of cylinders generated by the
classical L\"uroth expansion.
  Possible infinite entropy of the stochastic vector $Q_\infty$ which
determines the metric relations for partitions of the generalized L\"uroth
expansions, possible non-faithfulness of the family $\Phi(Q_\infty)$ and the
absence of general formulae for the calculation of the Hausdorff dimension even
for probability measures with independent identically distributed symbols of
generalized L\"uroth expansions are all facts that do not allow to apply usual
probabilistic methods, as well as methods of dynamical systems to study fractal
properties of corresponding subsets of non-normal numbers.
  Despite of the above mentioned difficulties, we develop new approach to the
study of subsets of $Q_\infty$-essentially non-normal numbers and prove
(without any additional restrictions on the stochastic vector $Q_{\infty}$)
that this set is superfractal. This result answers the open problem mentioned
in \cite{AKNT2} and completes the metric, dimensional and topological
classification of real numbers via the asymptotic behaviour of frequencies
their digits in the generalized L\"uroth expansion.

23
The categories of this paper are: solv-int
7
The categories of this paper are: hep-th
5
The categories of this paper are: gr-qc
21
The categories of this paper are: adap-org
34
The categories of this paper are: chem-ph
26
The categories of this paper are: bayes-an
28
The categories of this paper are: alg-geom
25
The categories of this paper are: patt-sol
0
The categories of this paper are: hep-ph
19
The categories of this paper are: eess
8
The categories of this paper are: hep-ex
3
The categories of this paper are: physics
10
The categories of this paper are: q-bio
27
The categories of this paper are: comp-gas
24
The categories of this paper are: dg-ga
22
The categories of this paper are: chao-dyn