Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On ergodic properties of iceberg transformations. I: Approximation and
  spectral multiplicity   We investigate a class of mixing dynamical systems around the concept of
iceberg transformation. In brief, an iceberg transformation is defined using
symbolic language as follows. We build a sequence of words such that the next
word is a concatenation of rotated copies of the previous word. For example, a
word CAT can turn into CAT.ATC.TCA.TCA.CAT.ATC, then we repeat the procedure
applying it to this new word and so on. Geometrically, given an invertible
measure preserving transformation $T$ an iceberg is a union of two icelets for
the map $T$, one direct and one reverse with common base set, where icelet is
defined in a similar way as Rokhlin tower $B \sqcup TB \sqcup \ldots \sqcup
T^{h-1}B$, namely, an icelet is a sequence of disjoint measurable sets $\{B_0,
B_1, \ldots, B_{h-1}\}$ such that the levels are nested: $B_{j+1} \subseteq
TB_j$. Reverse icelet is defined as icelet for $T^{-1}$, and it grows towards
the past. Iceberg transformation is approximated by a sequence of icebergs,
resembling the behaviour of rank one ergodic maps.
  It is show that a class of random iceberg transformations almost surely has
simple spectrum, $1/4$-local rank property and spectral type $\sigma$ such that
$\sigma \conv \sigma \ll \la$ where $\la$ is the Lebesgue measure on the circle
$S^1$.

8
The categories of this paper are: hep-ex
10
The categories of this paper are: q-bio
21
The categories of this paper are: adap-org
24
The categories of this paper are: dg-ga
20
The categories of this paper are: acc-phys
12
The categories of this paper are: nucl-th
3
The categories of this paper are: physics
29
The categories of this paper are: funct-an
1
The categories of this paper are: cs
7
The categories of this paper are: hep-th
17
The categories of this paper are: q-fin
5
The categories of this paper are: gr-qc
16
The categories of this paper are: stat
36
The categories of this paper are: cmp-lg
15
The categories of this paper are: nucl-ex
23
The categories of this paper are: solv-int