Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Statistical properties of topological Collet-Eckmann maps   We study geometric and statistical properties of complex rational maps
satisfying the Topological Collet-Eckmann Condition. We show that every such a
rational map possesses a unique conformal probability measure of minimal
exponent, and that this measure is non-atomic, ergodic and that its Hausdorff
dimension is equal to the Hausdorff dimension of the Julia set. Furthermore, we
show that there is a unique invariant probability measure that is absolutely
continuous with respect to this conformal measure, and we show that this
measure is exponentially mixing (it has exponential decay of correlations) and
that it satisfies the Central Limit Theorem.
  We also show that for a complex rational map f the existence of such an
invariant measure characterizes the Topological Collet-Eckmann Condition, and
that this measure is the unique equilibrium state with potential - HD(J(f)) ln
|f'|.

37
The categories of this paper are: supr-con
25
The categories of this paper are: patt-sol
19
The categories of this paper are: eess
5
The categories of this paper are: gr-qc
18
The categories of this paper are: econ
21
The categories of this paper are: adap-org
10
The categories of this paper are: q-bio
31
The categories of this paper are: ao-sci
36
The categories of this paper are: cmp-lg
33
The categories of this paper are: plasm-ph
3
The categories of this paper are: physics
35
The categories of this paper are: mtrl-th
13
The categories of this paper are: quant-ph
24
The categories of this paper are: dg-ga
0
The categories of this paper are: hep-ph
8
The categories of this paper are: hep-ex