UNSPECIFIED (1999) Common homoclinic points of commuting toral automorphisms. ISRAEL JOURNAL OF MATHEMATICS, 114 . pp. 289-299. ISSN 0021-2172

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Abstract

The points homoclinic to 0 under a hyperbolic toral automorphism form the intersection of the stable and unstable manifolds of 0. This is a subgroup isomorphic to the fundamental group of the torus. Suppose that two hyperbolic toral automorphisms commute so that they determine a Z(2)-action, which we assume is irreducible. We show, by an algebraic investigation of their eigenspaces, that they either have exactly the same homoclinic points or have no homoclinic point in common except 0 itself. We prove the corresponding result for a compact connected abelian group, and compare the two proofs.

Item Type:	Journal Article
Subjects:	Q Science > QA Mathematics
Journal or Publication Title:	ISRAEL JOURNAL OF MATHEMATICS
Publisher:	MAGNES PRESS
ISSN:	0021-2172
Date:	1999
Volume:	114
Number of Pages:	11
Page Range:	pp. 289-299
Publication Status:	Published
URI:	http://wrap.warwick.ac.uk/id/eprint/13744

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