Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The Fibonacci unimodal map   This paper will study topological, geometrical and measure-theoretical
properties of the real Fibonacci map. Our goal was to figure out if this type
of recurrence really gives any pathological examples and to compare it with the
infinitely renormalizable patterns of recurrence studied by Sullivan. It turns
out that the situation can be understood completely and is of quite regular
nature. In particular, any Fibonacci map (with negative Schwarzian and
non-degenerate critical point) has an absolutely continuous invariant measure
(so, we deal with a ``regular'' type of chaotic dynamics). It turns out also
that geometrical properties of the closure of the critical orbit are quite
different from those of the Feigenbaum map: its Hausdorff dimension is equal to
zero and its geometry is not rigid but depends on one parameter.

1
The categories of this paper are: cs
19
The categories of this paper are: eess
31
The categories of this paper are: ao-sci
11
The categories of this paper are: hep-lat
14
The categories of this paper are: math-ph
29
The categories of this paper are: funct-an
34
The categories of this paper are: chem-ph
25
The categories of this paper are: patt-sol
12
The categories of this paper are: nucl-th
20
The categories of this paper are: acc-phys
26
The categories of this paper are: bayes-an
15
The categories of this paper are: nucl-ex
22
The categories of this paper are: chao-dyn
4
The categories of this paper are: cond-mat
5
The categories of this paper are: gr-qc
33
The categories of this paper are: plasm-ph