Modified Jacobi-Perron algorithm and generating Markov partitions for special hyperbolic toral automorphisms (Q1321753)

R. Bowen pointed out that the boundaries of Markov partitions of hyperbolic toral automorphisms on \(T^ 3\) are not smooth. Furthermore T. Bedford has provided Markov partitions with fractal boundaries on a suitable subclass of hyperbolic toral automorphisms on \(T^ 3\), making use of the generating method of fractal curves of Dekking. The main idea is to construct a bounded domain \(X\) and a partition \(\{X_ i,i = 1,2,3\}\) on the expanding invariant plane with respect to a linear map \(L_ B^{-1}\) which induces the Markov endomorphism on \(X\) with structure matrix \(B\) by using the generating method of fractal curves. In the present paper the authors study the generating method of these domains with more accuracy.