Symplectic Partially Hyperbolic Automorphisms of 6-Torus
Dynamical Systems
2022-12-13 v1
Abstract
We study topological properties of automorphisms of a 6-dimensional torus generated by integer matrices symplectic with respect to either the standard symplectic structure in six-dimensional linear space or a nonstandard symplectic structure given by an integer skew-symmetric non-degenerate matrix. Such a symplectic matrix generates a partially hyperbolic automorphism of the torus, if it has eigenvalues both outside and on the unit circle. We study the case (2,2,2), numbers are dimensions of stable, center and unstable subspaces of the matrix. We study transitive and decomposable cases possible here and present a classification in both cases.
Keywords
Cite
@article{arxiv.2212.05110,
title = {Symplectic Partially Hyperbolic Automorphisms of 6-Torus},
author = {L. M. Lerman and K. N. Trifonov},
journal= {arXiv preprint arXiv:2212.05110},
year = {2022}
}
Comments
15 pages, 0 figures. arXiv admin note: text overlap with arXiv:2001.10727