Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Orbit equivalent substitution dynamical systems and complexity   For any primitive proper substitution \sigma, we give explicit constructions
of countably many pairwise non-isomorphic substitution dynamical systems
{(X_{\zeta_n}, T_{\zeta_n})}_{n=1}^{\infty} such that they all are (strong)
orbit equivalent to (X_{\sigma}, T_{\sigma}). We show that the complexity of
the substitution dynamical systems {(X_{\zeta_n}, T_{\zeta_n})} is essentially
different that prevents them from being isomorphic. Given a primitive (not
necessarily proper) substitution \tau, we find a stationary simple properly
ordered Bratteli diagram with the least possible number of vertices such that
the corresponding Bratteli-Vershik system is orbit equivalent to (X_{\tau},
T_{\tau}).

25
The categories of this paper are: patt-sol
32
The categories of this paper are: atom-ph
9
The categories of this paper are: nlin
27
The categories of this paper are: comp-gas
34
The categories of this paper are: chem-ph
16
The categories of this paper are: stat
33
The categories of this paper are: plasm-ph
11
The categories of this paper are: hep-lat
4
The categories of this paper are: cond-mat
8
The categories of this paper are: hep-ex
23
The categories of this paper are: solv-int
37
The categories of this paper are: supr-con
24
The categories of this paper are: dg-ga
19
The categories of this paper are: eess
28
The categories of this paper are: alg-geom
3
The categories of this paper are: physics