Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Continuity properties of folding entropy   The folding entropy is a quantity originally proposed by Ruelle in 1996
during the study of entropy production in the non-equilibrium statistical
mechanics. As derived through a limiting process to the non-equilibrium steady
state, the continuity of entropy production plays a key role in its physical
interpretations. In this paper, we study the continuity of folding entropy for
a general (non-invertible) differentiable dynamical system with degeneracy. By
introducing a notion called degenerate rate, we prove that on any subset of
measures with uniform degenerate rate, the folding entropy, and hence the
entropy production, is upper semi-continuous. This extends the upper
semi-continuity result from endomorphisms to all $C^r(r>1)$ maps.
  We further apply in the one-dimensional setting. In achieving this, an
equality between the folding entropy and (Kolmogorov-Sinai) metric entropy, as
well as a general dimension formula are established. These admit their own
interests. The upper semi-continuity of metric entropy and dimension are then
valid when measures with uniform degenerate rate are considered. Moreover, the
sharpness of uniform degenerate rate is also investigated by examples in the
scope of positive metric (or folding) entropy.

26
The categories of this paper are: bayes-an
29
The categories of this paper are: funct-an
11
The categories of this paper are: hep-lat
25
The categories of this paper are: patt-sol
17
The categories of this paper are: q-fin
14
The categories of this paper are: math-ph
36
The categories of this paper are: cmp-lg
28
The categories of this paper are: alg-geom
10
The categories of this paper are: q-bio
21
The categories of this paper are: adap-org
12
The categories of this paper are: nucl-th
37
The categories of this paper are: supr-con
16
The categories of this paper are: stat
24
The categories of this paper are: dg-ga
13
The categories of this paper are: quant-ph
3
The categories of this paper are: physics