homoclinic points of toral automorphisms - MathOverflow most recent 30 from http://mathoverflow.net 2013-05-21T01:41:41Z http://mathoverflow.net/feeds/question/65601 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/65601/homoclinic-points-of-toral-automorphisms homoclinic points of toral automorphisms ivo 2011-05-20T22:38:15Z 2011-09-17T12:22:12Z <p>Hi!</p> <p>Can you help me with solving this problem:</p> <p>Suppose that A is hyperbolic toral automorphism( represented with matrix A) with only one real eigenvalue \lambda >1 with geometric multiplicity 1. Suppose that v is right and w left eigenvector associated with \lambda and that =1. We construct a matrix H in the followig way. On position (i,j) matrix H has v_i w_j. I need to prove that set of homoclinic points to 0 of A is precisely p(Hm) where m belongs to Z^n and where p is a projection from R^n to n-dim torus T^n. </p> <p>Recall that point is homoclinic to 0 if both positive and negative iterates of A converge to 0.</p> http://mathoverflow.net/questions/65601/homoclinic-points-of-toral-automorphisms/66262#66262 Answer by Hanfeng Li for homoclinic points of toral automorphisms Hanfeng Li 2011-05-28T07:12:16Z 2011-05-28T07:12:16Z <p>See Example 3.3 of the paper ''Homoclinic points of algebraic Z^d-actions'' by Lind and Schmidt. </p>