Common homoclinic points of commuting toral automorphisms
Copyright policy )Common homoclinic points of commuting toral automorphisms
The homoclinic points of the hyperbolic automorphisms of the \(n\)-torus are studied. It is supposed that the automorphisms commute so that they determine a \(Z^2\)-action which is assumed irreducible. Then it is shown that every two automorphisms either have exactly the same homoclinic points or have no homoclinic points except 0 itself. The case of a compact connected abelian group is considered separately and the results are compared with those obtained for nonabelian compact groups.
- University of Vienna Austria
- Schrödinger United States
- University of Warwick United Kingdom
1010 Mathematics, homoclinic points, 1010 Mathematik, Unitary representations of locally compact groups, \(n\)-torus, compact groups, irreducible representation, hyperbolic automorphisms, Measure-preserving transformations
1010 Mathematics, homoclinic points, 1010 Mathematik, Unitary representations of locally compact groups, \(n\)-torus, compact groups, irreducible representation, hyperbolic automorphisms, Measure-preserving transformations
selected citations These citations are derived from selected sources.This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).1 popularity This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.Average influence This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).Average impulse This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.Average
Citations provided by BIP!Popularity provided by BIP!