Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Geodesics and dynamical information projections on the manifold of
  H\"older equilibrium probabilities   We consider here the discrete time dynamics described by a transformation
$T:M \to M$, where $T$ is either the action of shift $T=\sigma$ on the symbolic
space $M=\{1,2,...,d\}^\mathbb{N}$, or, $T$ describes the action of a $d$ to
$1$ expanding transformation $T:S^1 \to S^1$ of class $C^{1+\alpha}$ (\,for
example $x \to T(x) =d\, x $ (mod $1) $\,), where $M=S^1$ is the unit circle.
It is known that the infinite-dimensional manifold $\mathcal{N}$ of equilibrium
probabilities for H\"older potentials $A:M \to \mathbb{R}$ is an analytical
manifold and carries a natural Riemannian metric associated with the asymptotic
variance. We show here that under the assumption of the existence of a
Fourier-like Hilbert basis for the kernel of the Ruelle operator there exists
geodesics paths. When $T=\sigma$ and $M=\{0,1\}^\mathbb{N}$ such basis exists.
  In a different direction, we also consider the KL-divergence
$D_{KL}(\mu_1,\mu_2)$ for a pair of equilibrium probabilities. If
$D_{KL}(\mu_1,\mu_2)=0$, then $\mu_1=\mu_2$. Although $D_{KL}$ is not a metric
in $\mathcal{N}$, it describes the proximity between $\mu_1$ and $\mu_2$. A
natural problem is: for a fixed probability $\mu_1\in \mathcal{N}$ consider the
probability $\mu_2$ in a convex set of probabilities in $\mathcal{N}$ which
minimizes $D_{KL}(\mu_1,\mu_2)$. This minimization problem is a dynamical
version of the main issues considered in information projections. We consider
this problem in $\mathcal{N}$, a case where all probabilities are dynamically
invariant, getting explicit equations for the solution sought. Triangle and
Pythagorean inequalities will be investigated.

22
The categories of this paper are: chao-dyn
5
The categories of this paper are: gr-qc
9
The categories of this paper are: nlin
27
The categories of this paper are: comp-gas
29
The categories of this paper are: funct-an
0
The categories of this paper are: hep-ph
4
The categories of this paper are: cond-mat
11
The categories of this paper are: hep-lat
20
The categories of this paper are: acc-phys
3
The categories of this paper are: physics
26
The categories of this paper are: bayes-an
31
The categories of this paper are: ao-sci
28
The categories of this paper are: alg-geom
34
The categories of this paper are: chem-ph
32
The categories of this paper are: atom-ph
16
The categories of this paper are: stat