Block conjugacy of irreducible toral automorphisms. Issue 2 (3rd April 2019)

• Record Type: Journal Article
• Authors: Bakker, Lennard F.; Martins Rodrigues, Pedro
• Is Part Of: Dynamical systems. Volume 34:Issue 2(2019)
• Page Start: 244
• Page End: 258
• Publication Date: 2019-04-03
• Subjects: Irreducible toral automorphisms -- block conjugacy -- weak equivalence of ideals; 37C15 -- 13A15 -- 15B36; Differentiable dynamical systems -- Periodicals; 515.35205
• DOI: 10.1080/14689367.2018.1508553
• Languages: English
• ISSNs: 1468-9367

Abstract

ABSTRACT: We establish a matrix characterization (called block conjugacy) of the notion of weak equivalence of ideals. This gives the existence of a one-to-one correspondence between equivalence classes of block conjugate toral automorphisms (of a given irreducible characteristic polynomial) and equivalence classes of the weakly equivalent associated ideals. We show that there exist nonconjugate irreducible hyperbolic toral automorphisms A and B for whichA ⊕ A andB ⊕ B are conjugate.