Counting Berg partitions

Abstract

We call a Markov partition of a two dimensional hyperbolic toral automorphism a Berg partition if it contains just two rectangles. We describe all Berg partitions for a given hyperbolic toral automorphism. In particular there are exactly (k + n + l + m)/2 nonequivalent Berg partitions with the same connectivity matrix (k, l, m, n).

References in corpus (1)

• On the hyperbolic automorphisms of the 2-torus and their Markov partitions

Cited by in corpus (2)

• Elastodynamical properties of Sturmian structured media
• The Shortest Path Problem for the Distant Graph of the Projective Line Over the Ring of Integers